A wonderful goal from Josh Sheehan saw Wanderers take another major step towards securing a play-off place with a priceless three points.
Sheehan curled in a beauty 63 minutes into a one-side contest to give Wanderers the win they deserved and desperately wanted to open up some breathing space inside the top six with three games go.
The midfielder’s last goal had been a winner against Port Vale – the last time the Whites enjoyed a home victory at the end of February.
Ian Evatt’s men had drawn one and lost one at the University of Bolton Stadium since then ahead of a three-game home run which was possibly going to be the determining factor in their quest to extend their season.
And they made the perfect start to that trilogy thanks to Sheehan’s perfectly executed strike which brought to an end an hour of frustration.
The win should then have been more comfortable once Shrewsbury’s packed defences had been breached.
Heroics from Town keeper Marko Marosi - and the woodwork - made sure it wouldn’t quite be that way as he kept out a flurry of Wanderers’ chances.
But after dropping points to Cambridge in the previous home game there was to be no late lapse this time as James Trafford – who hadn’t needed to make a genuine save behind another rock-solid defence – chalked up his 21st clean sheet of the campaign and Wanderers edged closer to their target.
Wanderers – with Sheehan back in the line-up as the only change to the side that had started the mid-week draw at Burton – dominated possession from the start.
The Whites spent lengthy periods camped around the Shrewsbury penalty area but with a wall of blue and yellow shirts between them and the goal, it wasn’t easy to find a way through.
Sheehan was among those who saw plenty of the ball as Wanderers probed away and switched the ball from left to right.
But despite almost complete territorial advantage, Evatt’s men could only fashion two half-openings for Kyle Dempsey before the break as the midfield man found room for efforts he steered just wide.
Wanderers needed a spark and started the second half with a greater degree of urgency as they looked to penetrate down the flanks and expose a Town defence starting to feel the pace in their quest to avoid a sixth defeat in seven games.
And when they did work the ball into the box, Dion Charles was close to getting a touch on Sheehan’s delivery in front of goal.
For the first time it felt like the goal was coming and with 55 minutes gone Charles thought he’d got it.
Aaron Morley’s tackle sent the ball into the feet of the Whites' leading scorer, who dummied his way past the last defender but couldn’t beat Marko Marosi, who spread himself to save.
Charles did have the ball in the net moments later from a Conor Bradley cross but saw the effort disallowed for a push.
In all-out attack mode Bradley then saw a deflected shot bounce up against the crossbar before Dempsey’s header from the corner was superbly saved by Marosi.
The Shrews were clinging on for dear life but finally Wanderers’ pressure paid off as Sheehan broke the deadlock in spectacular style.
The little midfielder always wanted the ball and this time he went it alone, accepting a pass from Morley. looking up and from 25 yards out curling a beauty into the top corner to claim his second goal of the season.
That raised the decibels even further as the home fans lifted their team and they nearly on their feet again with 20 minutes to go.
The excellent Dempsey had just forced another save out of Marosi when he slipped the ball through for Victor Adeboyejo to face the Shrews’ keeper.
Again, though, Marosi made a terrific save to just about keep his side in the contest, although it would have been game over had a thumping volley from Charles gone under the bar rather than smacking against it with just under a quarter of an hour to go.
The Whites still needed the second goal to make sure and there were further chances, Marosi saving again from birthday boy Elias Kachunga ahead of stoppage time.
But anything other than maximum points would have been a travesty and with home games to come next against Accrington Stanley and Fleetwood, impressive Wanderers kept their fate very much in their own hands as they moved up to fifth place in the table.
Wanderers: Trafford; Jones, MJ Williams, Johnston; Bradley, Morley, Sheehan (Lee 75), R Williams; Dempsey; Charles (Kachunga 82), Adeboyejo (Nlundulu, 75). Substitutes: John, Shoretire, Thomason, Jerome.
Booked: MJ Williams
Shrewsbury: Marosi; Pennington, Dunkley, Moore, Shipley; Winchester, Leahy; Bloxham (Saydee 67), Phillips, Street (Bennett 67); Bowman. Substitutes: Burgoyne, Craig, Barlow.
Booked: Winchester, Bowman
Referee: Tom Reeves
Attendance: 18,596 (Shrewsbury 740)