Rugby Park was a hive of activity as Celtic ran riot at the other side of the country.
Jota's 30-yard screamer and Mortiz Jenz's acrobatic effort made it three at the half.
Carl Starfelt scored his first goal for the Celts.
35 games without a loss is the longest winning streak in the Scottish league.
They are still looking for their first win in the topflight.
The side that won in Dingwall did not need to be changed.
Within seven minutes, his decision was vindicated as Greg Taylor slipped in Daizen Maeda. The onrushing Kyogo finished a simple move off the post.
There was a question mark over Sam Walker and whether the Killie keeper could have done better after Jota scored the second.
He wasn't able to do anything about the third. The ball was thrown towards the goal. It was nice to see Jenz get his second goal in as many weeks.
It took the visitors more time to get their fourth, but they were content to let the game go on. Walker's save from a Celtic corner gave Starfelt the chance to score.
There was no debate about whether the goal was an overhead kick or not. A crossed ball looped into the sky, the Greek forward watched it onto his foot and then bicycle- kicked it through the legs of Walker for a classy fifth.
There's still a long way to go this season, but Celtic have started in a way that will make Postecoglou confident of retaining the title.
At times, they were so aggressive that they toying with them like a cat with a ball of string.
The test of two games a week will begin with the group stage of the European Championship. rotation isn't the threat it used to be because of the depth on the bench
The other teams in the league were warned. McInnes tried to match Celtic in a 4-3-3) formation. It didn't work as individual Celtic's stars showed a lot of quality in creating space for themselves.
Both Celtic and Kilmarnock are looking for their first win of the season on the same day.
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