Boyd struck on 73 minutes after Kris Doolan had levelled for Partick in the early stages of the second half following Chris Johnston's opener for the hosts.
The teenage winger struck three minutes before the break when he planted a low strike past the diving Scott Fox after Boyd failed to control a Rory McKenzie cross.
Thistle levelled the match on 49 minutes when Doolan weaved his way past Jeroen Tesselaar for a clear run at goal to place the ball past Craig Samson, who dived the wrong way.
And the visitors should have taken the lead when Steven Lawless blazed with the goal at his mercy, after an awkward bounce Christie Elliot's delivery.
Fox had an escape when he spilled substitute Michael Gardyne's strike without finding a Kilmarnock player sniffing about the rebound.
But within seconds, the Partick keeper had been beaten as Boyd got the faintest of touches to Jackson Irvine's long-range effort to divert the ball home.
Kallum Higginbotham should have beaten Samson after combining with substitute John Baird but was denied at point-blank range.