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.
With those sort of statistics, Celtic manager Neil Lennon kept changes to a minimum with Forrest and Pukki coming in for Nir Biton and Georgios Samaras.
There was no surprise that the champions took control of the game from the first whistle.
There was, however, some surprise that they were not awarded a penalty in the ninth minute when Killie skipper Manuel Pascali tugged the shirt of Kris Commons inside the box as the Hoops player tried to find space to get a shot away.
Referee Brian Colvin was unimpressed but what looked like a poor call was forgotten two minutes later when Forrest set up Ledley for the Wales international to drive the ball low past Samson and into the far corner of the net.
Killie had their own penalty claim when Hoops defender Virgil van Dijk clashed with William Gros but the incident looked to have taken place outside the box, although no action at all was taken.
It transpired to be a token attack by the Ayrshire side.
Celtic's second came in the 20th minute when Forrest turned Kilmarnock defender Jeroen Tesselaar inside out down the right-hand side before his cross was turned into his own net by the stretching Ashcroft.
The assault on Samson's goal continued.
In the 28th minute Parkhead skipper Scott Brown dispatched a ferocious shot from the edge of the box which the over-worked keeper brilliantly turned away for a corner, which he clutched out of the air to give his team mates some respite.
Four minutes from the break van Dijk came close with a drive from the edge of the box which skipped past Samson's left-hand post by inches.
Five minutes into the second-half Hoops keeper Fraser Forster was called into action for the first time to make a fine block from Pascali's close-range volley, after the Italian had latched on to a Sammy Clingan cross, with the England cap punching the resultant corner clear.
Celtic were far from rampant but the chances kept coming. Just before the hour mark, Commons floated a cross on to the head of Pukki at the back post but the Finland international headed over the bar.
In the 63rd minute Forrest teed up midfielder Mulgrew and his shot from 14 yards beat Samson but rebounded off the post and into the arms of the keeper.
However, the Scotland international had more luck when Ledley took a pass from Commons and dinked the ball over the Killie defence for Mulgrew to control and knock past Samson from six yards.
The Kilmarnock keeper then made a save from Pukki at his near post before the luckless Hoops striker was replaced by Balde but it was Commons who missed the next chance in the 78th minute when he toe-poked the ball past the post from six yards.
The final stages saw van Dijk miss a sitter after barging his way past a tired-looking Killie defence but in injury time Samson gifted Balde his goal by letting a weak shot through his grasp.