It was a much improved performance from Jim Jefferies' men, although Celtic were far removed from the devastating force they were against St Mirren on Saturday.
McDonald had the game's first chance after finding space on the right side of the Killie defence, but his shot flew just wide with the suggestion of a fingertip touch from Alan Combe.
Kilmarnock were starting to look comfortable with Kevin Kyle giving them a new dimension up front, but it was their weakness in central defence which cost them in the 27th minute.
Marc Crosas' incisive pass found McDonald in acres of space in the inside left channel inside the box and the Aussie ended the Celtic striker scoring crisis with an excellent controlled finish low into the far corner.
Killie failed to plug the gap as twice more within the next five minutes David Lilley was posted missing allowing first Scott Brown and then Aiden McGeady clean through.
Both should have scored but both were denied by great blocks from Combe, the latter being touched onto the crossbar.
In between these attempts, Killie's Jamie Hamill almost caught Artur Boruc out with a cross-shot which the Pole did well to tip over.
After being on the ropes for ten minutes, Killie found themselves level after Danny Invincibile was picked out in space behind a statuesque Celtic defence at a corner and planted the ball behind Boruc.
The second half was evenly contested with Celtic continuing to create the clearer chances.
The champions looked to have regained the lead in the 65th minute when Gary Caldwell met Shunsuke Nakamura's corner with a point-blank bullet header, but somehow Combe reacted to block the ball clear.
Kyle was at the heart of every good Killie move, but substitute Conor Sammon wasted their best chance when he missed his header from 12 yards.
It took a piece of magic to beat the Killie keeper and McDonald delivered it with only ten minutes left with a brilliant solo goal.
Collecting the ball on the edge of the box, he snaked and shimmied his way past two defenders before feigning to shoot and sending Combe the wrong way.