Midfielder Joe Ledley opened the scoring in the 11th minute of a desperately one-sided affair with an angled-drive before Killie defender Lee Ashcroft turned the ball into his own net from a James Forrest cross.
Midfielder Charlie Mulgrew grabbed a third in the 67th minute before substitute Amido Balde added a fourth in injury-time, helped by Killie goalkeeper Craig Samson, who let a less than powerful shot slip through his hands.
The Hoops have now gone 23 league games unbeaten since the start of the season to sit 18 points clear of second-placed Aberdeen, and another clean sheet means the champions equalled the club record of 10, last achieved in 1921/22.
CELTIC: Forster, Fisher, Ambrose, van Dijk, Izaguirre, Brown, Mulgrew (Johansen 82), Ledley, Forrest (Boerrigter 77), Pukki (Balde 71), Commons.
KILMARNOCK: Samson, Clohessy (O’Hara 53), Ashcroft, Pascali, Tesselaar, McKenzie, Clingan, Slater, Kiltie (Nicholson 46), Muirhead (Gardyne 76), Gros.
Referee: Brian Colvin.