After a battling Town performance, the away side suffered a late heartbreak, losing 2-1 away to Peterborough United on Tuesday night.
The home side took the lead through Jonson Clarke-Harris in the 17th minute, with the centre-forward heading in at the back post from a Joe Ward cross.
The Salop faithful only had to wait four minutes to get back on level terms, with Tom Flanagan smashing the ball against the underside of the bar and in from just inside the box.
Peterborough were awarded a free kick in the 87th minute, which Ward again took.
Kabongo Tshimanga flicked it on for Frankie Kent to head home what proved to be the winner.
Manager Steve Cotterill opted for a 4-3-3 formation at the Weston Homes Stadium.
With Killian Phillips unavailable following a nasty clash of heads in the draw at Derby, Carl Winchester came into midfield alongside Luke Leahy and Tom Bayliss.
And the boss also opted to give Tom Bloxham a first league start of the season - with the youngster starting on the left flank and Rekeil Pyke on the right. Christian Saydee was the central striker.
In defence, Matt Pennington started at right-back with Taylor Moore on the left and Chey Dunkley and Tom Flanagan partnered up the heart of the defence.
Darren Fergurson's Peterborough went with a 4-2-3-1 formation with Clarke-Harris in the centre-forward position.
Two free-kicks dominated the opening 20 minutes in Cambridgeshire.
It was the hosts who took the lead when Joe Ward whipped in a dangerous delivery that Clarke-Harris nodded in at the back post.
Town, though, were only behind for a couple of minutes - with Leahy this time sending a free-kick to the back post, which Dunkley headed across goal.
And that header was met by Flanagan, who emphatically smashed the ball against the underside of the bar and in.
Peterborough had a chance to regain the lead just past the half-hour mark when the ball broke kindly for Ward in the box.
His powerful shot, though, was well blocked by Marosi - with the keeper having positioned himself perfectly to keep the ball out.
Town then had a chance to take the lead just before the break when Bayliss delivered a wonderfully inviting ball to the back post.
That delivery, though, was just cut out by a defender with Pennington waiting to pounce.
Just before the hour mark, Jordan Shipley replaced Pyke, and the 25-year-old nearly made an immediate impact.
Bayliss flicked the ball onto Shipley just inside the box and unleashed a rocket that looked destined for the top corner, but a Posh defender blocked the effort.
A few minutes later, the ball fell to Bloxham on the edge of the area and picked out Bayliss, who was ready to pounce on the penalty spot, but the midfield couldn't keep his shot down.
With just over 20 minutes to go, the home side countered quickly down the left, with Mason-Clark showing his speed and trying to cut in, but Dunkley did fantastically to guide Posh's number 10 out of play.
The remainder of the half was dominated by counters for both sides, but late into proceedings, Peterborough were awarded a free kick that was again taken by Ward.
Substitute Tshimanga flicked on the set piece for Kent and he headed home the winner in the 87th minute.
Shrewsbury didn't give up and had a late chance to level when Leahy fizzed in a strike from 20 yards. Will Norris did well to parry away and secure all three points for the home side.
Teams
Salop XI:
Marosi (GK), Leahy (C), Pennington, Moore, Winchester, Pyke (Shipley, 57), Bloxham (Street, 86), Bayliss (Bennett, 86), Dunkley, Saydee (Bowman, 86), Flanagan
Unused subs:
Burgoyne (GK), Craig, Barlow
Peterborough United XI:
Norris (GK), Edwards, Kent, Taylor, Clarke-Harris (C), Mason-Clark, Thompson (Butler, 70), Ogbeta (Tshimanga, 82), Burrows, Kyprianou (Norburn, 90), Ward
Unused subs:
Blackmore (GK), Jones, Thompson, Randall
Bookings: Pyke, Flanagan, Saydee; Kyprianou, Norris, Norburn
Attendance: 7,388
Away: 313
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