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, on for Teemu Pukki after the break, 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.
Jamie Hamill's penalty gave Hearts back-to-back wins for the first time this season as they overcame 10-man St Mirren 2-1 in an absorbing contest.
Saints scored after just 30 seconds through Steven Thompson, but the hosts levelled two minutes later courtesy of Callum Paterson and gained the upper hand in the 52nd minute when Hamill converted from 12 yards after Marc McAusland had been shown a straight red card for fouling Dale Carrick.
Despite going a man down, the Buddies continued to threaten and Thompson passed up two more great chances in front of goal but they could not find an equaliser.
The win moved bottom side Hearts within 16 points of Partick ahead of Sunday's crucial League Cup semi-final against Inverness.