Sam Ricketts’ side dropped into the League One bottom four after the Highbury Stadium reverse, in which the visitors went close to a late equaliser and almost punished Fleetwood for not putting the game to bed.
Fleetwood were the better side after the 25th-minute opener and Salop had Harry Burgoyne to thank for some key saves either side of half-time.
Shrews went close through Brad Walker and Daniel Udoh at the end of a blustery evening but another defeat means they have won just one from eight league games this season.
It is the first time Shrewsbury have fallen to three straight defeats in regulation league games since April 2017.
Mark Pugh, the free agent who joined the club on Monday, was named on the left of Ricketts’ front three, making his second Shrewsbury debut, 13 years on from the first.
The left-sided attacker was reunited with his former Bournemouth left-sided colleague Charlie Daniels, as the pair combined to devastating effect, helping the Cherries from League One to the Premier League.
Pugh, 33, was turning out in blue and amber for the first time in 11 years and added to the 46 appearances in his first Salop spell.
Ricketts, in a bid to turn the tables after disappointing back-to-back home defeats, including Pugh as one of four changes from the side beaten by Rochdale.
Ryan Barnett joined him on the opposite side of the front three, replacing Jason Cummings, who was omitted from the squad. There were also recalls for Walker and Ethan Ebanks-Landell, replacing Scott High and Aaron Pierre.
Fleetwood were in good spirits on the back of an assured 2-0 win at Gillingham on Saturday, where potent forward pair Paddy Madden and Evans both netted.
Joey Barton’s men sat mid-table ahead of kick-off but boast a squad of real quality this season. Canada international Jayson Leutwiler was in goal for the Cod Army, facing Shrewsbury for the first time since his departure in 2017.
Swirling wind on the Fylde Coast meant high balls were caught in the elements as the two sides got going.
Barton’s men sent a couple of early deliveries into the Town box that the visitors, with Ebanks-Landell marshalling the backline, dealt with well.
Shrewsbury were lively and sharp without the ball. Josh Vela in particular typified a combative and purposeful start, winning the ball on multiple occasions. Ricketts and Dean Whitehead liked what they saw, Barton less so after 15 minutes.
Daniels and Pugh were quiet early on, with most of the play coming down Shrewsbury’s right. The heavens opened for driving rain midway through the first half at Highbury Stadium as both sides pushed in a physical contest lacking in moments in either penalty box.
But the hosts broke through 25 minutes in. They ventured down the left and left-back Danny Andrew got beyond Barnett and Marlon Fossey after a neat one-two.
Ex-Grimsby man Andrew showed good composure to send a low cross that travelled to Evans and the Wales international was deadly with his first-time finish beyond Burgoyne and in off the far post.
Town could not find the grit or bite in their attack in response as the ball struggled to stick in the front three.
The hosts, who were forced to replace the injured Jay Matete with Callum Camps after edging ahead, could have doubled their lead but Burgoyne made a crucial low stop to deny Madden.
Fleetwood were the more composed side as an unremarkable side played out. Shrewsbury struggled putting any passes together and were unable to offer any sort of threat as a forward line, with Udoh totally isolated.
Salop required better after the interval but were further indebted to goalkeeper Burgoyne for a sharp point-blank save to keep out Camps’ first-time finish after a left-sided move.
The worrying signs continued as Fleetwood were presented with yet another clear-cut opening after Walker lost it cheaply. Wes Burns was denied by another good Burgoyne save from a narrow right angle.
Shrewsbury needed a change and Ricketts rolled the dice, ending Pugh’s debut on 53 minutes and sending on Leon Clarke.
The visitors saw more of the ball but were still unable to find a decisive moment in the final third. Clarke chested for skipper Ollie Norburn whose deflected 25-yard shot straight at Leutwiler just after the hour was Town’s first effort on target.
Ricketts turned to Northern Irish attacker Josh Daniels to add some drive to the right of his front three.
But Shrews were grateful to Fossey’s positioning shortly after as the full-backs headed off the line from Evans’ deflected half-volley.
A succession of Charlie Daniels long throws led to little of a blue and amber persuasion, but Walker went closest to hauling his side level with a deflated drive from 25 yards that whistled just wide with 19 minutes to go.
Barton grew more agitated on the touchline as Shrewsbury threatened to make inroads in the home penalty box as Fleetwood stood firm to defend their slender lead.
Some pinball in the Fleetwood box from a good Fossey delivery dropped the way of Ebanks-Landell and the defender’s finish looked set for the bottom corner before being deflected off target.
The hard-working Udoh was fractions from a big equaliser with three minutes remaining but his spin and shot was brilliantly saved near the post by Leutwiler.
Defender Aaron Pierre was sent on to hustle Fleetwood’s defence in the dying moments but an equaliser eluded Shrewsbury, whose poor run of results continued.
Fleetwood Town (4-3-3):
Leutwiler; Edwards, Connelly, Mulgrew, Andrew; Matete (Camps, 27), Coutts ©, Duffy (Whelan, 61); Burns (Morris, 82), Evans, Madden.
Subs not used: Cairns (gk), McKay, Saunders, Holgate.
Shrewsbury Town (4-3-3):
Burgoyne; Fossey, Williams, Ebanks-Landell, C Daniels; Walker (Pierre, 89), Vela, Norburn ©; Barnett (J Daniels, 67), Udoh, Pugh (Clarke, 53).
Subs not used: Gregory (gk), High, Tracey, Zamburek.
Referee: Bobby Madley