Steven Whittaker then put the seal on the win with Rangers' third of the day to pile the pressure on Celtic ahead of their visit to Dundee United on Sunday.
The match was overshadowed slightly by the mystery which once again surrounded the whereabouts of Madjid Bougherra, amid reports he had failed to report back from international duty on time yet again.
The defender missed the SPL game at St Johnstone in October, claiming his delay in returning to Glasgow on that occasion was the result of his possessions, including his passport, being stolen.
Lack of matches for the Scottish champions recently meant he would not have been involved on Saturday anyway, but boss Walter Smith admitted: "I don't think it's his valuables that have been lost this time, it's him."
Kilmarnock came close early on when Garry Hay picked out Kevin Kyle in plenty of space in front of goal but, despite being handed a free header, the big striker was denied by the quick reflexes of goalkeeper Allan McGregor.
Instead, it was Rangers who took the lead after just seven minutes and it was no real surprise to see Boyd claim the opener and continue his impressive goalscoring form against his former club.
Kevin Thomson supplied a lovely pass which Boyd ran onto before calmly dispatching an angled drive past goalkeeper Mark Brown from just inside the box into the bottom corner of the net.
The striker had the net bulging again a couple of minutes later but the offside flag was raised before he had even unleashed the shot.
At the other end, another dangerous ball from Hay from the left found Manuel Pascali this time and McGregor was called into action again to prevent his volley from finding the back of the net.
Boyd turned provider when he set up Steven Naismith but his powerful, point-blank effort was blocked by Brown, with the on-loan Celtic keeper doing well to prevent the visitors falling further behind.
But he was helpless to deny Rangers their second of the day with 25 minutes on the clock. A long ball from Whittaker found Lee McCulloch, who knocked into the path of Miller for the striker to slot home from 12 yards.
Brown was plucking the ball out of the net again ten minutes later. Miller's cut-back found Whittaker and his first attempt was blocked by Frazer Wright, but he was able to rifle home the rebound despite the goalkeeper getting a hand to the ball.
Rangers managed to cause a few problems for Killie after the interval. A lovely ball from Boyd found Naismith out on the left who rolled a pass into the path of the onrushing Sasa Papac but the left-back's ferocious effort flashed across the face of goal and wide.
Boyd sliced an inviting ball through the Killie defence for Miller but his shot was weak and comfortably smothered, before Kyle Lafferty - who replaced Boyd - saw his looping header cleared off the line by Pascali.
With one eye on Tuesday's crucial Champions League game against Stuttgart, Miller was withdrawn for John Fleck, leaving just one of their goalscorers on the pitch for the remainder of the game.
Thomson was then denied the chance to add his name to that list of scorers when he collected from Lafferty only to rattle his shot off the foot of the far post but, by then, there was no way back for the visitors.