The match was effectively over after just half an hour as the Celts had found the back of the net four times.
Kyogo Furuhashi broke the deadlock after seven minutes and should have claimed an early brace, but the Japan star failed to convert a spot-kick a quarter of an hour later.
There was little to worry about, though, as compatriot Daizen Maeda doubled the Killie's deficit in the 12th minute.
Matthew O'Riley banged in a quick-fire brace with goals in the 18th and 27th minute to condemn the hosts to a 4-0 score-line.
Just before the break, Kilmarnock struck back through Liam Donnelly but it wasn't enough.
Celtic made a host of changes not too long into the second half and allowed the home side more of the ball.
The Killie were unable to make much use of it, though, and the visitors claimed their emphatic victory.
