Killie had the perfect start with a well-worked goal in the second minute. Danny Invincibile made the initial break down the right. Gary MacDonald joined the attack and he stood the ball up at the back-post, taking goalkeeper Gordon Marshall out of the play, where Colin Nish unselfishly nodded across the face of goal for Boyd to smash home his tenth goal of the season.
Alan Combe almost gifted an immediate equaliser when he fumbled a cross, but Simon Ford was on hand to block Kevin McBride's effort.
The keeper made amends in the 11th minute with two great saves. First he dived low to his left to finger tip Scott McDonald's fine long-range shot behind, then from the corner, clawed Steven Hammell's net bound cross-shot to safety.
Motherwell's midfield completely dominated the match and had Killie on the rack for long spells. They should have equalised in the 23rd minute when Martyn Corrigan's perfectly-timed pass sent McDonald and David Clarkson behind Killie's offside trap. McDonald carried the ball to the six-yard line but opted to set his partner up when it looked easier to score, and Ford used his pace to get back and hack clear.
Just as in last week's cup-tie, Killie scored on the stroke of half-time to double their lead. Peter Leven made the initial interception which sent Nish clear on the left. He worked it on to Boyd, who advanced into the danger area and finished expertly.
Leven could not shake off the effects of the tackle which set up the goal and had to be replaced early in the second half by Gary Locke.
Well's McDonald wasted another clear chance in the 57th minute when Freddy Dindeleux misjudged a long ball and allowed the striker a free run into the box. McDonald seemed to do everything right until he pulled his shot wide of the target.
Another lightning break gave Motherwell a clear view of goal just after the hour mark. This time Clarkson was the man as he took the ball round Combe, but he could only find the side net from an acute angle.
McBride's free-kick skimmed the roof of the net, but frustrated Motherwell could not find even a consolation strike.