The Bairns were outplayed in the first half but Darren Barr headed them in front 11 minutes after the break.
The visitors looked set to climb off the foot of the table but goalkeeper Dani Mallo let Kyle's 20-yard strike squirm through his hands midway through the second half.
Falkirk did cut the deficit at the bottom to two points after St Mirren lost to Motherwell, while Killie remain embroiled in an intriguing relegation battle.
The hosts could have ensured a six-point lead over Falkirk before half-time on Saturday as they squandered a series of chances.
Kyle had been suspended since scoring all three goals when the teams met last month and he was central to an impressive first-half display.
Kyle and Willie Gibson came in for the injured Danny Invincibile and David Fernandez, while Falkirk had to make an 11th-minute change when Michael Higdon replaced Mark Stewart, who failed to return to the action after being accidentally caught in the face by Garry Hay's arm.
Hay had just been denied a penalty by referee Alan Muir following a challenge from Scott Arfield, who appeared to take some of the ball as well as felling the Kilmarnock skipper.
Kyle was showing some good touches to bring wide men Gibson and Mehdi Taouil into the game and the striker was also proving a threat inside the box with two headers comfortably saved by Mallo in the opening 15 minutes.
David Lilley produced a brilliant diving headed clearance to stop Neil McCann's cross reaching Higdon but Falkirk's attack proved a brief interlude in constant Killie pressure.
Kyle had several more efforts at goal and he should have done better when he headed Taouil's corner over from eight yards.
Tim Clancy could have set the former Sunderland striker up for a shooting chance after robbing McCann deep inside the Falkirk half, but his pass got caught under Kyle's feet.
Jamie Hamill also squandered a decent chance when he volleyed over from 12 yards after Simon Ford had nodded down Taouil's free-kick.
Kyle then glanced Clancy's long free-kick just wide after a great leap and his best chance of the half came seconds later in the 39th minute.
Gibson's cross found the target man unmarked eight yards out but Mallo blocked his downward header.
Craig Bryson set up Hamill in a quick break in injury-time and Mallo pushed away the midfielder's powerful strike from 20 yards.
Lee Bullen replaced Jackie McNamara in Falkirk's right-back position for the start of the second half.
The Bairns took a shock lead with their first effort on target as Barr beat Alan Combe to McCann's near-post corner and headed into the empty net.
Kilmarnock were struggling to attain the fluency of their first-half display but Kyle levelled in the 67th minute.
Combe's kick-out broke to the striker off Gibson 20 yards out and his first-time strike bounced into the net, despite Mallo getting both hands to the ball.
Kyle's shot was far from his most powerful effort of the day but the goalkeeper was slow to get down.
Falkirk soon had a decent penalty claim rejected when Hamill nudged a leaping Barr, who then almost grabbed a second goal which would have been a carbon copy of his opener.
The defender again met McCann's corner but Combe pushed the ball behind his near post.
Killie also had a great chance to win it in an exciting finale but Kyle's header sailed inches wide following a cross from Hay.
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