For long periods Falkirk held the upper-hand after James Fowler had opened the scoring with a spectacular long-range strike against the run of play.
So there was a sense of justice when Kenny Milne scrambled home an equaliser only for Boyd to underline his value with a late tap-in to give Kilmarnock their third away victory in a row.
Falkirk have now gone ten games this season without a home victory but this could well have been the match they broke their duck.
They were a victim of failing to turn their possession into goals and Alan Combe contributed to their downfall with a handful of fine saves.
Boyd dragged an early chance wide after a mistake by Milne but Falkirk looked livelier and Alan Gow fired wide from the edge of the box.
Then Pedro Moutinho produced a fine turn and curling shot that brought a left-handed save from Combe.
The chief sinner in front of goal for Kilmarnock was Steven Naismith who missed a couple of glorious first-half opportunities before firing wide from only 15 yards at the beginning of the second period.
But midfielder Fowler showed him the way to goal with a brilliant solo effort after 48 minutes. He picked the ball up on the halfway line and ran unchallenged before firing a 25-yarder into the top corner of the net.
It was a stunning strike that could have knocked the wind out of Falkirk's sails, but they came back strongly.
And after Combe had produced a magnificent save from Andrew Lawrie's header, Milne was on hand to stab home the rebound.
Falkirk looked far more likely to grab a winner as they camped in the Kilmarnock half, but Allan Johnston broke away deep into injury time to test Matt Glennon with a long-range effort.
Unfortunately for the keeper, he could only parry Johnston's shot out into the path of Boyd, who made no mistake from six yards.