The test against Hearts ended with nine men and Celtic moved two points clear at the top of the table.
The first half was dominated by the hosts, but only one goal was scored.
After the break, Hearts improved and disrupted Celtic's rhythm before losing two players.
Giorgos Giakoumakis won in the final moments.
It keeps Celtic's perfect start of four straight victories.
The line-up for the second leg of the play-off reflected the importance of the game.
There were seven changes from the first-leg defeat in Switzerland for the second leg.
The visitors fell behind in the first 15 minutes.
After Daizen Maeda wriggled clear of Cochrane and whipped over a cross from the right, Kyogo was left alone six yards out to volley past Stewart.
Before the break, Hearts regrouped and manfully prevented further damage, with Jota lashing into the side-netting, Matt O'Riley knocking an acrobatic effort wide and Maeda planting a headed chance into Stewart's arms.
Josh Ginnelly had a chance to open the scoring but he dragged his shot wide of the goal.
As Celtic started the second half poorly, the visitors' belief grew as well. Ginnelly failed to connect with Alan Forrest's ball across the face of goal, while Sibbick couldn't connect with the ball.
Even after throwing on McKay and Shankland for the final half hour, Hearts were unable to trouble Joe Hart, as they failed to record a single shot on target.
Celtic's search for a second goal was stopped by Stewart's save from O'Riley, with substitute Hatate scoring the rebound. When Giakoumakis bundled in Josip Juranovic's delivery, he was able to get through.
Celtic had to overcome a patchwork Hearts side.
The hosts were careless with the ball in the second half and gave their visitors a foothold.
Celtic's defensive solidity saw them through the rocky patch, with a third clean sheet secured while limiting the visitors to a measly XG.
Celtic had plenty of chances to make the game safe before Giakoumakis scored. Is the Greece forward going to start next weekend after scoring in successive games?
A glance at the teamsheet shows that the manager's priorities this week are elsewhere, with no risk to his main men.
The early concession could have opened the door, but Hearts dug in and knocked Celtic off their stride after the break.
The Edinburgh men's plucky efforts came to nothing as they were bereft of cutting edge.
There wasn't a lot of flow to the game. It was difficult to get going. We did some of it ourselves.
Even though it was 0-1 for a while, I never felt threatened. The keeper kept them in the game.
The players came in and I was happy with them. We have quality in the depth of the squad, even though we don't have a large squad.
We played well for a long period of time. We're in a good position if the referee doesn't send our players off.
The second leg of the play-offs will be held at Tynecastle on Thursday, and Hearts are hoping for a home advantage.
On the same day, Celtic will play their first game of the season at home against Dundee United.
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