Carlisle recorded their first win of the season at Gay Meadow following a solid defensive performance and quality finish from Ian Stevens.
The Cumbrians had to defend for long periods but were strong when required and produced the best move of the match after 83 minutes to win the game.
Carl Heggs looked to have handled in midfield but rode his luck to feed Scott Dobie down the right. Dobie got to the byeline and whipped a cross into the feet of former Shrewsbury favourite Stevens, who volleyed home.
Jubilant manager Ian Atkins said: "This win will give the lads the confidence they have been lacking so far. We competed for every ball and Richard Prokas and Steve Soley were outstanding in midfield. The players started to believe in themselves in the second half.
"The goal was the best move of the match and we will try to take the positive things into our match at Kidderminster on Saturday."
The match started brightly, both sides going close. A fourth-minute Ross Davidson header clipped the Carlisle bar, but the visitors should have taken the lead after seven minutes when a through-ball from Prokas found Dobie in space but he shot weakly with only Town keeper Ian Dunbavin to beat.
Former Sunderland winger Sam Aiston was seeing a lot of the ball down the Shrewsbury left and proved a constant threat to the Cumbrians' defence. A 16th-minute slip by Julian Darby let in Chris Freestone who pulled his shot wide.
Freestone again went close on 42 minutes when his header was cleared off the line by Darby. On 49 minutes Freestone broke free only to see his shot saved by Weaver.
As Carlisle came more into the game, Dobie headed wide on 71 minutes from a Mark Birch cross.
The result will give the Cumbrians a timely boost with another difficult away game at the Aggborough Stadium on Saturday.
Shrewsbury Town: Dunbavin; Jenkins, Hanmer, Peer, Hughes, Davidson, Jagielka (Brown 79), Thomas, Freestone, Jemson, Aiston. Subs not used: Edwards, Lowe, Wilding, Murray.
Scorers: None
Bookings: Davidson (86)
Carlisle United: Weaver; Birch, Whitehead, Darby, Winstanley, Hemmings (Pitts 52); Soley, Prokas; Dobie, Stevens (Lee 89), Heggs (Lee 53). Subs unused: Tracey, Carss, McAughtrie.
Scorers: Stevens (82)
Bookings: Dobie (54), Darby (71),Soley (90)
Attendance: 2,912
Referee: A. Wiley (Burntwood)
