A first half which had been tightly contested with little goalmouth action sprang to life when home skipper Sean Long scored from close range and then, within a minute of the restart, Alfie May fired in a second to leave Salop with it all to do.
Unfortunately they were unable to build up any real of head of steam to trouble the Cheltenham defence following an afternoon which needed a pre-match reshuffle with Luke Leahy moving to left back due to the absence of George Nurse and Jordan Shipley.
Shrewsbury boss Steve Cotterill made four changes – three of them enforced - which included the hugely disappointing pre-match news that Nurse’s injury has been diagnosed as a ruptured ACL ligament ruling him out for the remainder of the season.
Nurse’s absence was felt even more keenly given Shipley, who would have been expected to move to left back, had to depart the squad a couple of hours before kick-off after his wife went into labour.
Skipper Leahy reverted back to the left wing back position which he has occupied previously in his career.
Keeper Marko Marosi was also absent with the finger injury picked up during last week’s win against Burton Albion, giving Harry Burgoyne his first league start since May, 2021.
Tom Flanagan returned to the side after his international duty with Northern Ireland, Elliott Bennett came in for his first league start of the season, and Ryan Bowman was preferred to Rekeil Pyke up front.
The hosts produced an early threat with a long throw from Ryan Jackson leading to a corner which was taken short before being sent into the box, Matthew Pennington on hand to head clear.
Shrewsbury’s first real attack on five minutes almost fashioned an opening, Christian Saydee trying to cushion Leahy’s crossfield pass into Tom Bayliss’ path but getting too much on the header, giving keeper Luke Southwood the chance to gather.
Bayliss was almost in again minutes later after Bowman held the ball up well before feeding Saydee to drive at the defence and then look to slide in the midfielder.
Bayliss was facing some close attention from the retreating Cheltenham defence and his shot was blocked at source.
It had been a fairly quiet opening to the game but the home fans were united in their disapproval of a robust challenge on Jackson from Flanagan in the 18th minute which earned the Salop man a booking.
Flanagan was in the right place to head away the resulting free kick and Chey Dunkley the same from another Jackson long throw a few minutes later as the Shrewsbury defence were given a test of their aerial capabilities.
Leahy was on the end of a couple of strong challenges and after the second, adjudged a foul, Liam Sercombe became the first Cheltenham player to go into referee Carl Brook’s book.
Burgoyne had cleanly claimed a couple of crosses during an otherwise quiet first half hour but found himself diving to cover his angles when Cheltenham midfielder Ryan Broom let fly from distance shortly afterwards.
Broom got plenty of power on his long-range effort but not quite the accuracy as it flashed over the crossbar.
Leahy was looking sprightly for Salop down the left-hand side and flew towards goal after anticipating a back-header from Jackson only for keeper Southwood to once again be alert and quickly off his line.
It was a case of the ‘three B’s’ combining for Shrewsbury when Flanagan’s clearance set Bowman away down the right.
The striker played the ball inside cleverly for Bayliss whose first-time pass found Bennett before the Cheltenham defence managed to block his intended ball for Saydee.
With 90 seconds remaining the game’s first big chance of the half arrived, and Salop were indebted to the reflexes of Burgoyne to keep the scores level.
Another Jackson long throw was flicked goalwards by Lewis Freestone and Burgoyne was well placed to tip the ball over.
But the keeper could do nothing just a minute later as another long throw came in from which the hosts took the lead.
Another long throw, this time from Will Ferry on the opposite flank, was flicked on and skipper Sean Long was first to the ball to tap home from close range.
It had been a tight first half with nothing between the two teams and little for either keeper to do but that goal just before the break gave Cheltenham a big boost to take into the interval.
And it was a boost they carried into the very first minute of the second half by extending their lead.
A neat move ended with Alfie May’s clinical first-time volley from Jackson’s right-wing centre crossing the line via the underside of the crossbar giving Shrewsbury everything to do for the remainder of the game.
The hosts were now oozing confidence and it needed the Salop defence to stay strong as May’s driven effort from the left was deflected wide.
After seemingly weathering the initial storm Salop then went on search of a way to get back into the game but there was no one in the box to meet a couple of promising first-time driven crosses from Leahy.
Saydee was continuing to battle up top in a bid to unsettle the Cheltenham back-line and won a free kick just outside the box as the hour mark approached.
But Leahy’s effort after Bayliss stopped the ball was always heading over the top and didn’t give Southwood anything to do.
Midway through the half Cotterill made his first change with Pyke being brought on for Bowman, and then switched to a 4-2-3-1 formation in an effort to try and help Salop become more of an attacking force.
Although Shrewsbury then started to pass the ball far better, they were still struggling to make attacking inroads and the next big chance fell to Cheltenham, Dan Nlundulu wriggling his way down the inside left and trying his luck from an acute angle with a shot which flashed wide of the post.
At the other end a decent Shrews move saw Bennett find Leahy whose cross was just overhit too strong before Carl Winchester tried an ambitious left foot effort which he dragged comfortably wide.
With four minutes remaining, as May looked to have suffered a serious injury and was stretchered off with Taylor Perry coming on, Salop made another change with Flanagan making way for Aiden O’Brien.
There were a total of seven minutes of added time during which Julien Da Costa was sent on to replace Bennett and Salop won a corner from which Pennington’s header drifted wide.
But in truth there had never looked like being a way into the game and a difficult day at the office for Shrewsbury ended in a 2-0 defeat on the road.
CHELTENHAM (3-5-2): Southwood; Freestone, Taylor, Long; Ferry, Sercombe, Bonds, Broom, Jackson; May (Perry 89), Nlundulu (Lloyd 83).
Subs not used: MacDonald (gk), Williams, Bradbury, Brown, Norton.
SALOP (3-5-2): Burgoyne; Pennington, Flanagan (O’Brien 86), Dunkley; Bennett (Da Costa 90+3), Moore, Winchester, Bayliss, Leahy; Saydee, Bowman (Pyke 67).
Subs not used: Bevan (gk), Street, Bloxham, Caton.
Referee: Carl Brook