The striker's finish was inch-perfect, but Killie boss Jim Jefferies will be unhappy that McDonald was completely unmarked as he received Crosas' pass in the penalty area.
Within minutes Combe came to his team's rescue twice as Celtic exploited gaping holes in the right side of Killie's defence.
First the keeper blocked Scott Brown's close-range effort, then he deflected Aiden McGeady's low shot on to the crossbar.
Celtic were made to rue their wastefulness in front of goal on 36 minutes when Invincible side-footed past Boruc, with the visitors failing to deal with Craig Bryson's corner.
Five minutes after the restart Celtic's defence were almost punished a second time for failing to attack a high ball.
David Fernandez should perhaps have done better than lob over the bar with Boruc advancing, but the early chance seemed to lift the home side.
Kilmarnock began to find more space in attack and could have taken the lead on two further occasions before the hour mark through Kevin Kyle and Connor Sammon, who badly miscued a free header from 12 yards out.
At the other end Combe produced another fantastic save to deny Gary Caldwell's bullet header at point-blank range.
But with nine minutes remaining McDonald showed wonderful skill to turn Lilley on the edge of the box before toe-poking the ball in from 12 yards to give Celtic a vital victory.
Kilmarnock manager Jim Jefferies:
"I thought we were terrific, 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 the players to knock it in behind them, and when we 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 took a class goal like that 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."
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