Salop dominated the opening 55 minutes of the game having numerous opportunities to score.
But the controversial sending-off of defender Tom Flanagan in the 55th minute - changed the direction of the match.
The centre-back was given two yellow cards at the same time, which saw Salop go down to ten men.
And just after Salop had sent on talisman Daniel Udoh on 76 minutes, a cross by Mitch Clark from the right was headed in by Leigh to secure all three points for Accrington.
Town welcomed Stanley to the Meadow for their first home game of the season.
The visitors would have been buoyed by a 96th-minute equaliser they scored against Charlton last weekend.
And Salop were boosted ahead of kick-off when star striker Daniel Udoh was fit enough to make the bench.
The fan favourite has not featured for Town since they played Burnley at Montgomery Waters Meadow in pre-season earlier this summer.
But the same could not be said for summer signing Aiden O'Brien. He was not fit enough to make his home debut at the Meadow - even though he came on for 10 minutes at Morecambe last weekend.
Steve Cotterill named an unchanged starting eleven that managed a point away at Morecambe.
Matthew Pennington, Chey Dunkley and Flanagan were the back three, with Julien Dacosta and George Nurse playing as the wingbacks.
Skipper Luke Leahy and Taylor Moore again made a midfield two.
And Jordan Shipley and Tom Bayliss played in support of number nine Ryan Bowman.
The occasion also marked the first time Salop legend Shaun Whalley returned to the Meadow. The winger made 257 appearances for Town in his seven years at the club.
Both sides enjoyed a bright start, but the first chance went to Shrewsbury.
A corner was whipped in from the left by Bayliss, and Leahy attempted an ambitious overhead kick. He scuffed his attempt, but the ball fell to Pennington who had a shot blocked.
Shortly after, Bayliss showed nice feet in midfield to send Dacosta away down the right. His cross found Bayliss again in the box, but he could not turn his effort to goal, and it went just wide.
Salop began to assert their dominance in the game, and on 17 minutes, Nurse played a great ball over the top, and Bowman found himself through on goal, but the forward took too long with his shot, and Rich-Baghuelou got back in time to make the block. The Accrington defender injured himself making the block and had to be replaced by Ryan Astley.
Just before the half-hour mark Taylor Moore found himself in half a yard of space, he played a great diagonal pass over Stanley's fullback to Dacosta, who made his way down the right and put a cross in towards Bowman. The forward did well to turn his effort goalwards, and it forced a smart stop out of Lukas Jensen.
Shrewsbury piled on the pressure and they had another great chance to take the lead. It was again down the right-hand side, with Dacosta being at the centre of everything Salop did well. He played a pass to the edge of the box, and Shipley helped the ball on its way to Bowman, but his effort from 10 yards went agonisingly wide.
Accrington's only major chance of the half was a fierce strike from Ethan Hamilton from 35 yards. It was an ambitious effort but he hit it well and forced Marosi into a smart stop. Turning the ball over.
Salop kept on banging on the door, and inside five minutes of additional time, Shipley let rip a strong shot which was palmed away by Jensen after a cleverly worked corner routine with Bayliss.
It was another good half of football for Town. The only thing missing was a goal.
Such was Shrewsbury's dominance that Accrington manager John Coleman rung the changes at halftime.
But regardless of that Salop started the half on the front foot.
Bayliss and combined again down the right-hand side and the wingback won a fifty-fifty challenge on the edge of the Stanley penalty are. Dacosta made his way into the penalty area and his strike was heading for the bottom corner. But again, it was saved brilliantly by Jensen.
However, for all Salop's good work the complexion of the game changed when defender Tom Flanagan was sent off after being shown two yellow cards at the same time.
It was after several players got involved in pushing and shoving the Salop box. The confrontation all started goalkeeper Marosi pushed an Accrington player to the floor. The referee consulted his colleague and sent Flanagan from the field.
As a result of the red card, the game became more stretched. And after Shrewsbury had dominated the first 55 minutes, it allowed Accrington back into the contest.
Daniel Udoh made his return on 75 minutes when he came on for Bowman.
For all Salop's good play in the game, it was Stanley who took the lead.
A cross by Mitch Clark came in from the right, and sub, Tommy Leigh rose the highest to head the ball into the corner.
A hammer blow for Town.
Chey Dunkley had a chance to level from a corner but he couldn't get enough on the header to get his effort on target.
And despite Town trying their best to get back into the game, they could not manage to create a clear-cut chance that would earn them a deserved draw.
Salop: Marosi, Pennington, Dunkley, Flanagan, Nurse, Dacosta, Moore, Leahy, Shipley (Bloxham 84mins), Bayliss (Pyke 78 mins, Bowman (Udoh 76mins).
Accrington: Jensen, Clark, Rich-Baghuelou (Astley 20mins), Hamilton, Coyle (Conneely), Whalley (Adedoyin 71mins), Lowe, Pritchard (Leigh 45mins), McConville, Sangare (Longelo 45mins), Rodgers.