McDonald opened the scoring but Danny Invincible levelled just before the break.
However the Australian international had the last word in an entertaining second half with a late winner.
"I thought we were terrific," said Kilmarnock boss Jim Jefferies. "But I was disappointed at their first goal because McDonald is their main striker and he was on his own.
"We had two great chances, from David Fernandez and Connor Sammon.
"David should have stuck it away, and Connor should have chested it down, but in the end it was a complete fresh-air header.
"But how could you fault our team tonight?
"Normally we like to get the ball down and pass it, but I said to them to knock it in behind them and when did that we always gave them problems.
"I can fault my players for the first goal, but the second was piece of magic from McDonald - it was a class goal like that it took to beat us tonight.!
Celtic manager Gordon Strachan: "We said a couple of weeks ago there would be twists and turns and I'm sure that's not it finished yet.
"I thought we were absolutely fantastic, we couldn't have started any game better than we did tonight.
"The players were terrific, they could have panicked after Kilmarnock got the goal back, but they kept playing the right game.
"Kilmarnock hung in there, showed good determination, and the guys up front were always a threat with the longer ball they were playing.
"For his second goal Scott was twisting and turning and we were thinking 'lay it off', and then we thought 'no - keep going'.
"But I think it's going to be an exciting run-in for the title."