Kilmarnock recorded their second win in four days to leapfrog their visitors in the league table.
Both sides passed up golden opportunities to opening the scoring in a sterile first half.
Kilmarnock's offside trap was sprung in the 11th minute, but Steve Lovell lost his composure in front of goal and dragged his shot wide.
Killie's Craig Dargo's miss was even worse in the 24th minute after the best move of the half. Alan Mahood clipped the ball neatly to the far post where Chris Innes unselfishly laid the goal on a plate for Dargo, unmarked three yards out.
But somehow Dundee keeper Julian Speroni managed to scramble across his goal-line to save at his feet.
Dargo had a horrible match, with nothing going right for him and it was no surprise when he was substituted in the 55th minute.
The change worked for Kilmarnock as it was Dargo's replacement Stevie Murray who set up the chance for Stevie Fulton to score within two minutes of coming on. The little winger's cross broke back to Fulton on the edge of the box and the skipper blasted an unstoppable shot past Speroni.
Jim Jefferies had brought on Boyd at half time and the young striker sealed the win in injury time.
Content to run down the clock the home side passed the ball around, but Jamie Fowler spotted Boyd in acres of space and the striker made no mistake slotting the ball home from 20 yards.