James Forrest's return from injury added fresh attacking impetus to Neil Lennon's side and he played his part in the first two goals before Charlie Mulgrew and Amido Balde completed the scoring.
The Hoops scored a stylish opener in the 11th minute as Forrest spun away from his marker before his threaded pass allowed Joe Ledley to fire past Craig Samson.
Forrest was again the creator when Celtic doubled their lead, his jinking run caused chaos before the winger's dangerous cross was turned into his own net by Lee Ashcroft (21).
Killie were struggling to hold the hosts at bay and Scott Brown's shot drew a decent save from Samson, while Virgil van Dijk's fierce effort flew over.
Celtic finally had some cause for concern after the break, with Manuel Pascali's volley forcing Fraser Forster into action, but the Hoops regained command and Mulgrew's shot hit the post.
The full-back was not frustrated for long as a clever chip from Joe Ledley picked out Mulgrew (68), who confidently clipped the ball past Samson.
Kris Commons dragged the ball wide as Celtic kept up their assault in the closing stages and substitute Balde (90) added a fourth when his shot slipped through Samson's grasp.