The former Rangers and Aberdeen winger set up Conor Newton to fire home a first-time effort in the 78th minute and then struck an impressive goal three minutes from time.
The victory moved Saints level on 27 points with Kilmarnock and ended a run of five consecutive defeats for the Paisley side.
Saints had been the better team in a dire first half but both sides had chances in a far more entertaining second period and Kris Boyd hit the post for Killie in between the goals.
St Mirren were without suspended captain Jim Goodwin and they left Eric Djemba-Djemba on the bench.
They started the game on the front foot but they rarely got in behind their opponents in the first half, although they created several half-chances while Killie were devoid of an attacking threat.
Paul McGowan failed to connect properly with a Steven Thompson knockdown and Josh Magennis saw a shot deflected just wide by Jeroen Tesselaar after trying to turn the Dutchman.
Kenny McLean provided the best piece of quality of the half when he fired a 35-yard free-kick just wide.
Kilmarnock were not helped by losing Sammy Clingan to injury in the 26th minute following a fierce challenge with Sean Kelly. Jackson Irvine came on and Allan Johnston made another change at half-time when Robbie Muirhead replaced Alexei Eremenko.
The forward took 30 seconds to do what his team-mates had failed to do in the first 45 minutes - get a shot on goal. But his long-range effort was comfortably held by Marian Kello.
Thompson got a header on target but Craig Samson dealt with his first save with little trouble.
McGowan provided him with a far greater test in the 53rd minute when he ran at Lee Ashcroft and attempted to steer the ball in the far corner from 16 yards but the former Saints goalkeeper got down well to push the ball wide.
Good close control from Newton set up another chance for Magennis and Samson fumbled his shot wide.
Another good run from McGowan set up Newton but the midfielder's failure to pull the trigger 18 yards out infuriated the provider and the fans.
Kilmarnock were far more effective going forward than the first half and Muirhead sent a curling left-footed shot towards the far corner, which Kello pushed away.
McLean and Irvine skied efforts as the game became more stretched.
Ashcroft soon headed over after a deep cross from Chris Johnston, who then made way for on-loan Sunderland winger David Moberg Karlsson to come on for his Kilmarnock debut.
McGowan sent a first-time effort over the bar before being replaced by Wylde and the winger soon set up the opener when he came in from the left and played the ball across the 18-yard line.
Thompson failed to connect but Newton ran on to the ball and this time showed no hesitation to steer a first-time effort inside the near post.
Killie had a great chance to equalise two minutes later when Craig Slater's through ball sent Boyd clear and the former Rangers striker's deft touch sent the ball past the onrushing Kello but against the post.
And Wylde made sure of the points when he intercepted a pass midway inside the Killie half and ran at the defence before unleashing a powerful 20-yard strike that bounced in off the far post.