In a breathtaking performance, a Kris Commons double and a Gary Hooper strike had the points tied up for the visitors before the interval.
Anthony Stokes scored a fourth at the start of the second half and in the end the punch-drunk Ayrshire side were happy not to concede any more goals.
After such a convincing victory Celtic, who have a game in hand over Rangers, will travel to Ibrox on Sunday for the last Old Firm clash of the season in confident mood.
The mood around Rugby Park before tonight’s game with Killie was peculiar.
Most of the attention was on Neil Lennon after morning revelations that parcel bombs had been sent to him, a lawyer and a politician.
The Hoops fans behind both goals sang in support of their boss and they had something to cheer in the fourth minute when the electric Commons fired them into the lead.
Hooper slipped the ball to the Scotland midfielder who dispatched his shot from just inside the box so quickly that Killie goalkeeper Anssi Jaakkola had no chance.
The visitors were clearly fired up and Kilmarnock, try as they might with some neat passing, could barely get out of their own half.
In the 12th minute Commons flashed a shot from distance over the bar before, in Killie’s first real attack moments later, striker William Gros cut the ball back from the byline after going past Commons but found no takers.
Then David Da Silva tested Fraser Forster from close range after playing a one-two with midfielder Alexei Eremenko, but the Celtic goalkeeper blocked with his feet.
After another orchestrated vocal show of support for Lennon from the travelling support which was acknowledged by the former Hoops skipper, Commons drove wide from a narrow angle.
It was only a matter of time before the second goal arrived and in the 34th minute, after midfielder Jamie Fowler was caught in possession by Commons, Hooper again set him up and the former Derby player confidently slipped the ball past Jaakkola.
It looked all over for the bedraggled home side four minutes from the break when Hooper drove in number three.
The former Scunthorpe striker took a pass from Stokes, eased past Manuel Pascali and rifled a shot home from the edge of the box with the help of a slight deflection.
There was no respite for Killie in a whirlwind start to the second half.
From a Commons corner, Stokes forced a save from Jaakkola seconds before Commons’ angled shot from the edge of the box crashed off the crossbar.
In the 49th minute Stokes clipped the bar with a curling shot which had beaten the beleaguered Jaakkola, who soon had to deal with an effort from James Forrest, in for the injured Joe Ledley.
Stokes eventually got himself on to the scoresheet in the 58th minute after Charlie Mulgrew’s long pass down the left found Hooper, who controlled the ball and laid it off to the former Sunderland striker to drive high past the hapless Jaakkola.
Killie were all over the place as the Celtic support celebrated a sparkling performance from their side while anticipating more goals.
Celtic were toying with Killie at times and in the 70th minute the overworked Jaakkola had to make a decent save from Hooper’s point-blank drive.
The visitors were not for letting up and Forrest came close with an angled drive from the edge of the box with two minutes remaining which sped past the far post.
There was no addition to the scoreline and Lennon took the acclaim of the Celtic supporters at the end of the match.