Steve Cotterill’s men turned it around against the Dons after Dapo Mebude broke away to finish a slick visiting counter-attack from a desperately poor short Town free-kick.
Town left wing-back Luke Leahy cancelled out that first-half opener with a fine looping header for his first Shrewsbury goal just before the break.
It appeared Shrews may record a third 1-1 draw on the spin in League One before Udoh - introduced for Sam Cosgrove on 64 minutes - rose three minutes later to head in superbly from Leahy’s cross to a deafening Montgomery Waters Meadow roar.
The comeback win, just Town’s second in nine league games this term, lifted Cotterill’s men out of the relegation zone to 20th.
Udoh answered his manager’s call with a priceless winner in the first of back-to-back Saturday-Tuesday home fixtures as Town hunt wins to climb from the foot of the table that have proven elusive so far this term.
Shrewsbury will hope an injury that forced star midfielder Josh Vela off in the second half is not serious, while Cotterill’s men again were required to rally as the search for a first clean sheet of the corner goes on, now stretching into a 12th game.
But the victory, sealed reasonably comfortably at the death with few clear chances for in-form Wimbledon due to some excellent defending, extends Town’s excellent record against the visitors. Salop have no not lost in 12 against the Plough Lane club, and 12 attempts.
The victory will be of relief to Cotterill, his staff and Town players after the hosts fell behind in extremely poor fashion, as short free-kick in Dons’ territory failed to come off and the visitors broke four or five-on-one to devastating effect as Watford loan youngster Mebude swept in emphatically.
Town were good value for their leveller before the break having had the better of an open first half. The second period did not bring as many opportunities, but Udoh clinically stuck away a huge moment for his side.
And it was Udoh’s name ringing around a jubilant Meadow at full-time as the home crowd responded as vocally as they have at the end of any fixture so far this term.
The importance of the three points was not lost on anybody inside the Meadow, as the hosts hope victories are easier to come by moving forward.
For the first time in the league this season - in the ninth game - Cotterill named an unchanged Town line-up.
After scoring his first goal for the club in the draw at Sheffield Wednesday, Ryan Bowman kept his place in the forward line alongside Sam Cosgrove.
The Town chief kept his wing-backs in place after Elliott Bennett and Leahy had been instrumental in goals against Crewe and the Owls.
Shrewsbury’s one change on the bench was Harry Burgyone in for Cameron Gregory after serving a three-match suspension.
Salop were out to protect their excellent head-to-head record against the Dons, whom they had lost against just once - May 2012 after League Two promotion was sealed - in 13 attempts.
The visitors were riding something of a wave and started the day seventh in the table, with just two defeats - both 1-0 - from their opening eight games.
Mark Robinson’s men had also enjoyed an excellent EFL Cup run too, which came to an end in the third round at Arsenal’s Emirates Stadium on Wednesday night, less than 72 hours ahead of kick-off in Shropshire.
Robinson - the club’s former youth set-up manager who took the top job in February and led a fine recovery - made three changes for the trip to Town. Top scorer Jack Rudoni dropped to the bench, as did physical striker Ollie Palmer.
Anticipation was in the air at the Meadow after a period of applause to remember the late Jimmy Greaves. Cotterill had issued a rallying cry for home fans to show similar support to that of the visiting faithful at Hillsborough last week, and the Town fans in safe standing in particular were in good voice early on.
The youthful Wimbledon side - with the youngest average age in the division at 23 years - were predictably lively in the opening stages.
The hosts allowed midfielder Anthony Hartigan too much room in the middle of their half, but Hartigan’s strike from distance flew well wide.
Moments later left winger Dapo Mebude should have done better when unmarked in the box from the lively Ayoub Assal’s pass, but his wires were crossed.
Shrewsbury responded in an open first 10 minutes and should have led themselves, but for a mixture of unconvincing finishing and goalkeeper Nik Tzanez heroics.
The visitors could not clear a Town free-kick and Shaun Whalley - operating in the ‘No.10 role’ - saw his low strike parried away by Tzanez only to Ethan Ebanks-Landell amid a crowded box, but the skipper’s first-time rebound was too central and Tzanez saved again at the second attempt.
Backed on by good noise from a couple of hundred ardent Dons followers, both sides shared a couple of set-pieces - with Cotterill’s side forcing referee James Bell into one or two soft decisions.
The manager had revealed he had been working his players on defending set-pieces, which have proven an Achilles heel on a few occasions this season.
Cotterill said set-pieces are a particular strength of the visitors, but Ebanks-Landell and Matt Pennington cleared with good headers as Town went about preserving a first clean sheet.
Wimbledon forged their first big chance of the contest midway through the first period.
And, in what would not be for the first time in the afternoon, the visitors broke forward from a Town attack - down the hosts’ left - to break into their own left flank, where a cross was not sufficiently cleared and dropped to striker Aaron Pressley.
The frontman, from a slight ring angle, drove a fierce strike goalwards and Marko Marosi was forced into his first real action of the day with a good parried save, taking a bang in the face in doing so.
Referee Bell waved away a half-decent penalty shout for a possible push on Whalley before another presentable chance came the way of the hosts.
Bennett’s delivery from the right towards the back post was perfect and Bowman read the flight well as it dropped over his defender, but the striker could only send his diving header the wrong side of the left post.
Then, with 32 minutes on the clock, the home side fell behind through the poorest goal they have conceded this season.
Shrews were awarded a free-kick midway through the Dons half on the left flank and tried to be clever in working a short, quickly-worked set-piece.
Josh Vela, Leahy and Bennett combined from the short set-piece but the move broke down as wires were crossed and Dons looked to spring a break.
The visitors darted forward like the Red Arrows and quickly realised they had a four or five to one man advantage on Town.
A couple of accurate, splitting passes later, the latter from Town old boy Luke McCormick, saw Mebude played through on goal with just Marosi to beat and the winger swept into the corner with a fine first-time finish.
From their own free-kick, in the blink of an eye and in no more than five seconds, AFC Wimbledon led and the home fans were vocal in airing their frustration at the manner of the opener. Discontent and boos could be heard.
Town followed up that shocker with another free-kick, just overhit, as fans again voiced their frustration.
Shrewsbury desperately needed something before half-time and, four minutes before the interval, pulled level through a deserved equaliser.
They worked a move down the right and Bennett, recovering from losing the ball for Wimbledon’s goal, floated over a deep cross from the right touchline and there was opposite wing-back Leahy to climb and loop an excellent header over Tzanez and perfectly into the bottom right corner. Cotterill turned away with a clenched fist.
Salop ended the half in the ascendency and probably didn’t want the whistle to come.
Workhorse Vela saw a shot blocked on the edge of the box before Whalley spurned a golden opportunity.
A deep cross from the left was recycled by Cosgrove at the back post, who pulled back for Whalley, but the No.7’s effort while unmarked from no more than six yards out was rather scuffed and tame, straight at Tzanez.
The hosts required a big second 45 minutes if they were to turn a potential third draw on the spin into a victory required.
The second half began as open as the first, with the visitors shading possession and breaking into dangerous areas. It appeared Town found defending transitions difficult as Dons continued to look lively on the break.
The beginning of the second period lacked the goalmouth action that went before it, with a couple of niggling injuries and booking for Assal.
McCormick flashed well wide from distance for Wimbledon before, to real concern for Shrewsbury, Vela dropped to the deck on halfway following a challenge on halfway.
The influential midfielder attempted to continue for the best part of five minutes, but it became increasingly evident he was struggling.
While the midfielder toiled on the hour, Wimbledon upped the ante and Marosi was at his best to deny Dons frontman Pressley. The keeper got down to his bottom right corner to keep out a downward header before defender Ben Heneghan nodded wide at the back post from a corner.
Cotterill made two changes, with George Nurse on for Vela - with Leahy switched to the middle - and Udoh for Cosgrove.
Within barely 180 seconds of his introduction, Town fans’ favourite Udoh had come up trumps with an excellent and potentially priceless header.
A Town corner went uncleared before Leahy delivered an inch-perfect cross from the right flank where Udoh pounced to punish the costly error from Tzanez in coming out of his goal to claim, only to be beaten by the Town striker, whose header was a fine one.
Udoh wheeled away instantly to the Shrewsbury faithful who had chanted his name all afternoon. The roar was deafening.
Town tails were up despite Dons boss Robinson making a triple change - including Rudoni - and it was almost 3-1 with 20 minutes left as Bowman and Udoh combined well for the former to curl just wide of the far post from a narrow left angle.
The visitors attempted to rally and really should have equalised with 17 minutes left as the Shrewsbury centre-halves were deceived by the flight of the ball and Rudoni met the ball with a diving header but could only divert wide of the left post in front of an agonizing away end.
But, beyond Rudoni’s header and an excellent Bennett recovery challenge to steer McCormick’s low strike off target, Wimbledon’s late push came to very little with no more clear openings.
That was mostly thanks to an excellent late team effort from the home side, who remained resilient and compact and gave nothing to the visitors, an effort recognised by the joyous home crowd after the full-time whistle.
Shrewsbury Town (3-5-2):
Marosi; Pennington, Ebanks-Landell ©, Pierre; Bennett (Daniels, 90), Davis, Vela (Nurse, 64), Leahy, Whalley; Bowman, Cosgrove (Udoh, 64).
Subs not used: Burgoyne, Ogbeta, Leshabela, Bloxham.
AFC Wimbledon (4-2-3-1):
Tzanaz; Alexander, Nightingale, Heneghan, Guinness-Walker (Lawrence, 68); Hartigan (Marsh, 68), Woodyard ©; McCormick, Assal, Mebude (Rudoni, 70); Pressley.
Subs not used: Oualah, Csoka, Chislett, Osew.
Attendance: 5,346 (314 AFC Wimbledon fans)
Referee: James Bell