An early free kick from Thomson caused the home defence all sorts of problems with Madjid Bougherra inches away from diverting the ball home and Kirk Broadfoot, perhaps distracted by his team-mate, glancing it wide from close range.
Killie were full of energy and a lovely lay-off from David Fernandez presented Willie Gibson with a good shooting chance only for the midfielder to blaze wildly off target from the edge of the penalty area.
Rangers were fortunate to win a penalty on 28 minutes when Boyd collapsed under a challenge from Grant Murray.
However, Combe produced a fine save to keep out the striker's powerful spot-kick.
Boyd is not one to dwell on missed opportunities and soon after he rattled the crossbar with a venomous strike from 30 yards.
The woodwork came to the home side's rescue again when Nacho Novo hit the base of the post with a shot after controlling a clever pass from Pedro Mendes on his chest.
The Spaniard's effort cannoned back against the legs of the diving Combe and the keeper reacted quickly enough to prevent the ball from reaching Boyd.
Boyd was claiming for another penalty when Combe fumbled at his feet then grazed the striker with a flapping glove as he tried to recover the situation.
With a host of defenders frantically sliding back to cover the unguarded net, Boyd chose to tumble rather than shoot and a great opportunity was gone.
Frazer Wright made great challenge to block from Miller as the speedy Rangers striker broke clear after the half-time break.
But the visitors were ahead on 50 minutes when a deep corner reached the stooping Weir, who shrugged off Donovan Simmonds to crash in a header.
Three minutes later, Miller released Boyd with a fabulous cross-field pass and Boyd cracked home a sweet first-time finish from 18 yards.
Kilmarnock continued to work hard but lacked menace in front of goal and Combe remained the busier keeper, making saves to deny Broadfoot and Boyd.
With ten minutes remaining, Combe sliced down the charging Broadfoot but went unpunished; referee Eddie Smith flashing a yellow card at the luckless defender rather than awarding a penalty.
Miller headed in a Davis delivery from close range and Whittaker finished off Broadfoot's cross with a flying volley as Killie collapsed in the closing minutes.
There was a sour note on a good day for the visitors, with Thomson leaving the field on a stretcher after a crunching late clash with Fernandez.
Earlier, Kilmarnock's Jamie Hamill was on the receiving end of a bad tackle from Kyle Lafferty and also had to be replaced.
Sandy's Match Pic's are HERE
