Rangers took the lead in the ninth minute thanks to a dubious penalty decision.
Simon Ford tackled Boyd and knocked the ball out for a corner, but referee Dougie McDonald pointed to the penalty spot.
Boyd ignored the uproar and gave Alan Combe no chance by tucking the ball inside the keeper's right-hand post.
Former Killie striker Boyd reminded the home fans what they were missing on the half-hour mark when he rose at the far post to bullet home Alan Hutton's perfect cross.
Nacho Novo came on to partner Boyd at half-time and almost had an immediate impact but was denied by Combe.
The ball broke to Chris Burke with the goal at his mercy, but James Fowler made a dramatic goalline clearance.
Rangers full-back Hutton then gifted Kilmarnock a penalty when he sent Steven Naismith sprawling when there was no danger.
Peter Leven took the kick but Allan McGregor saved brilliantly to his right.
The Ibrox men swept upfield and, after Novo was barged over by Fowler for another spot-kick, Boyd repeated his first-half effort and scored in the same corner.
Killie got one back in the 73rd minute when Rangers' old failing at crosses came back to haunt them.
Paul Di Giacomo swung in a corner and it fell to Naismith on the line who bundled the ball home.