The striker bulleted in a first-half header from Mehdi Taouil’s cross and swept home three minutes after the break from a Willie Gibson pass.
St Mirren netted a late consolation through Dennis Wyness but now find themselves a point adrift of Falkirk at the bottom after their win at Hamilton.
Kilmarnock named an unchanged team for the crucial bottom-six battle as Rugby Park manager Jim Jefferies stuck with the starting side that earned a battling draw against Falkirk four days ago.
St Mirren made two changes from the side that slumped to a 3-1 home defeat by Motherwell at the weekend.
Will Haining was in defence in place of injured captain Jack Ross, who he replaced at half-time on Saturday, and Gary Mason started with Stephen McGinn relegated to the bench.
The match was keenly contested from the outset as both teams went in search of an early opener and St Mirren had some promising opportunities in quick succession around the 10-minute mark.
Andy Dorman curled a free-kick from the left wing narrowly wide of the opposite post, Hugh Murray’s cross from the right just evaded Dennis Wyness as he stretched to bundle it in at the opposite side, and then Dorman saw a drive from outside the area fly over the bar.
Kilmarnock’s best effort at that stage was a promising Garry Hay cross from the left byline that was cleared from Jamie Hamill – but they took the lead in convincing style after 22 minutes.
Taouil fired in an inviting cross from the left wing and Kyle arrived at speed to bullet home a headed opener.
Kilmarnock were forced to withdraw Simon Ford just before the half-hour and he was replaced in defence by Frazer Wright.
Kyle had another effort 10 minutes from the interval – Hay took the free-kick after Gavin Skelton was brought down by Murray but the striker’s header was this time easily claimed by Mark Howard.
St Mirren had a half-chance when Dorman combined well with David Barron but the defender’s acute-angled cross was easily dealt with by Alan Combe, while Wyness’ turn and shot never troubled the goalkeeper.
Kilmarnock doubled their lead three minutes into the second half when Kyle netted his second goal of the game.
Gibson set up the goal by sprinting up the left and holding off John Potter to work his way into the box then pass to the well-placed striker, who made no mistake as he confidently swept home.
Dorman forced Combe into a good save just before the hour, connecting well with Murray’s pass and shooting from an acute angle on the right, but the home goalkeeper was alert to beat it away from his near post.
Scott Cuthbert then headed a Dorman corner just wide as the visitors tried to reduce the deficit, and a scramble in the six-yard box greeted another set-piece from the midfielder, this time from the left-hand side.
The hosts continued to have plenty of possession and pressure – Taouil looked set to score from eight yards but his rising shot was blocked by Haining, and Howard was equal to Skelton’s corner.
St Mirren strung together a good passing move with 15 minutes to go but Cuthbert’s cross overshot all of his team-mates in the box as they attempted to set up a grandstand finish.
Dorman fired in a 25-yard free-kick five moments later but Cuthbert was the player who eventually put it over in a crowded box.
Gibson ran half the length of the pitch as Kilmarnock counter-attacked from a late Dorman free-kick and found Kyle in the centre but he put his eventual shot over the bar.
Substitute Wyness pulled a goal back for St Mirren in the final minute with a close-range effort following Dorman’s blocked shot – and the Paisley side had the ball in the net from an injury-time corner but the whistle had blown for a foul before the ball crossed the line.