Town’s winless run of 20 league games against their hosts was extended as Adam El-Abd and Joe Jacobson struck first half goals to cancel out former Chairboy Aaron Amadi-Holloway’s first Town goal.
Shrewsbury fell further behind after the midpoint of a fairly uneventful second half but top scorer Fejiri Okenabirhie netted to immediately bring Town back into it.
But managerless Salop were unable to rally again and were condemned to their first defeat in six games and since the sacking of John Askey.
It also means a barren league spell against the Buckinghamshire side, dating back to January 1994, was extended.
Coyne’s unchanged Town, lining up less than 72 hours after the FA Cup win at Salford on Wednesday, looked jaded in the first period and were unable to build on Amadi-Holloway’s third-minute opener.
The defeat drops Shrews one place to 17th, but they remain four points above the drop zone.
The hosts benefited from the compact nature of the middle of League One as they jumped from 15th to 12th in the third tier.
Excluding a Checkatrade Trophy trip to Crewe, Coyne’s Shrewsbury used the unchained XI that has served them well in the FA Cup against Salford and last time out in the league with Rochdale.
Town were concerned about a number of injuries after Wednesday’s win in Manchester, particularly with the quick turnaround before the trip to Adams Park.
But midfielders Greg Docherty, Anthony Grant, Ollie Norburn, forward Aaron Amadi-Holloway and defender Omar Beckles all recovered from knocks to be passed fit.
Both teams’ records had been almost identical this season, with just a point separating the 15th-placed Chairboys and Town below them.
But both Wanderers and Salop had picked up impressive runs of form going into the Adams Park meeting. Gareth Ainsworth’s men were searching for a fifth-straight home league win, while Coyne had guided Shrews to a fine three wins from three wins in temporary charge.
The hosts’ were hindered without their talismanic forward Adebayo Akinfenwa, who missed out with an injury, while on-loan Shrews midfielder Bryn Morris was not permitted to feature.
There was a debut in goal for emergency loan goalkeeper David Stockdale - who was between the sticks for Southend when Town won their first game of the current League One season.
Town were clearly not held down by the weight of history at Adams Park.
Chairboys dangerman Fred Onyedinma had already whistled one just wide from distance inside a minute before Amadi-Holloway announced himself back at Wycombe after barely 180 seconds.
Fejiri Okenabirhie ran the right channel to win possession and patiently measured an accurate cross on to the head of the big Town strike who climbed to head powerfully towards the bottom right corner.
Stockdale did not cover himself in glory. The on-loan Blues keeper got down to his left in good time but saw the ball squirm in near the post - not an ideal start to his Wycombe spell.
The travelling Salopians responded with great noise camped in behind the goal Amadi-Holloway had just found.
It was just the ex-Wycombe striker’s second league goal in two years and his first in competitive action for Shrews.
Town’s early opener had stemmed some attacking impetus from their hosts but any thoughts of a first clean sheet under Coyne in Buckinghamshire were undone by another former player.
With 11 minutes on the clock the visitors were unable to properly clear a corner, which was recycled to Chairboys skipper El-Abd who controlled on his chest before hammering a low volley beyond Arnold on the stretch.
Like Shrewsbury’s opening goalscorer, it was just the defender’s second goal in two years.
The watchable encounter settled down after an early flurry and one particular battle emerging was Okenabirhie against El-Abd, with the striker’s raw pace always likely to pose a threat to the 34-year-old.
El-Abd was booked at the second time of bringing down the lively Salop forward, leaving him treading a tightrope for the remaining hour.
Shrewsbury were struggling to knit passes together and play through the midfield as they have in recent weeks. The noticeable increase in energy under Coyne was not as apparent.
Wycombe’s pace was hurting Town. Onyedinma, Nathan Tyson, Alex Samuel and Jason McCarthy were useful outlets with their speed.
Coyne’s men found some useful positions before the break but were lacking a final pass, as they often went astray.
And it was almost out of nowhere that a third former player haunted their old employers.
There seemed little threat when Welshman Jacobson, a popular figure at the Meadow, picked up the ball between the left corner flag and the box, but he steadied himself and sent a delicious right-footed curled strike into the opposite top corner.
It was the left-back’s fourth goal of the season and a first from open play.
The away end looked on shell-shocked but Town could have found themselves immediately level. Luke Waterfall was inches from adding to his three goals this season but cracked the post with an unmarked far post header from Greg Docherty’s corner.
Town looked a little jaded after their midweek exploits amid a busy schedule and were in need of an injection of energy at the break.
The second half began with a noticeable show of support for temporary boss Coyne, as the Town crowd sang the name of the goalkeeper coach for a good 10 minutes, almost without taking breath.
A bitty second half did not get going until the hour mark, where Coyne rolled the dice significantly to bring on wingers Alex Gilliead and Abo Eisa for Docherty and Josh Laurent, who had been quiet.
Town went 4-4-2, with Eisa playing his first league football of any meaning of the season.
The visitors required a spark and the introduction of the two wingers had done little to change proceedings.
But, as the game entered its final 20 minutes, another flurry of goals gave the away end a lift.
Coyne will have looked on disappointedly as Wycombe attacked down Shrewsbury’s right, with Eisa, Josh Emmanuel and Waterfall easily bypassed as the Chairboys broke into the left side of the box and Samuel thrashed in a firm low finish.
But two minutes later Town profited from a needless Wanderers error. Two players ran into each other in the hosts’ half and Ollie Norburn broke before picking the right pass for Okenabirhie to slot into the far corner left footed.
It was the top scorer’s seventh goal of the season.
But Wycombe looked the more likely to add to their tally in the final 10 minutes and across more than seven minutes of alloted added time.
Town’s joyous period under Coyne came to end but supporters remained in fine voice with their backing for the Shrewsbury goalkeeper coach.
1 - Fred Onyedinma cuts in from the left side and unleashes a rocket which flies narrowly wide of Steve Arnold’s left post.
3 - Goal Shrewsbury. Fejiri Okenabirhie works hard to retain possession on the right before sending in a fine cross that was powered in by the head of Aaron Amadi-Holloway. Keeper David Stockdale should do better down to his left.
11 - Goal Wycombe. A recycled corner is looped back on to the edge of Town’s box and former captain Adam El-Abd chests down before volleying low beyond Arnold in style.
30 - Nathan Tyson connects to a deep Jason McCarthy cross from the right but can only volley off target from an extremely tight angle.
40 - Goal Wycombe. Joe Jacobson, who made 119 appearances over three years for Town, curled a superb right-footed effort into the opposite top corner from in between the left corner flag and the penalty box.
42 - Close to an instant equaliser as Luke Waterfall sends a diving bullet header against the post after being found unmarked at the back post from Greg Docherty's corner.
71 - Goal Wycombe. Poor defending down Town’s right allowed forward Alex Samuel space inside the box and he finished hard and low beyond Arnold. Game over?
73 - Goal Shrewsbury. Perhaps not game over. Ollie Norburn profits from a Wycombe error before playing in Okenabirhie who slotted in confidently.
82 - El-Abd wasted a chance to seal it as he headed over from a corner.
86 - Midfielder Dominic Gape’s effort from distance whistled over Arnold’s crossbar.
Wycombe Wanderers (4-4-2):
Stockdale; McCarthy, Jombati, El-Abd ©, Jacobson; Freeman, Gape, Thompson, Onyedinma; Samuel, Tyson (Williams, 67).
Subs not used: Yates (gk), Stewart, Mackail-Smith, Cowan-Hall, Harriman.
Shrewsbury Town (4-4-2 diamond):
Arnold; Emmanuel, Waterfall, Sadler ©, Beckles; Grant, Norburn, Docherty (Gilliead, 61), Laurent (Eisa, 61); Okenabirhie, Amadi-Holloway (John-Lewis, 83).
Subs not used: Coleman (gk), Bolton, Sears, Colkett.
Attendance: 4,598 (450 Shrewsbury fans)
Referee: Andy Haines
Star man: Fejiri Okenabirhie. Created one and scored one.
Position in the table - 17th (21 points from 19 games)