Killie striker Eamonn Brophy scored in the seventh minute with a penalty he won when he was fouled by returning Hoops defender Jozo Simunovic.
News of second-placed Gers' 2-2 draw against St Johnstone in Perth enthused the home fans and amid a Hoops siege, defender Kristoffer Ajer levelled from close range in the 29th minute before French striker Odsonne Edouard scrambled in four minutes later with defender Kirk Broadfoot in attention.
Hoops fans watched Neil Lennon's side play against 10 men from the 56th minute when Killie midfielder Alan Power, already booked, was sent packing by referee Kevin Clancy for his challenge on right-back Jeremie Frimpong, before striker Leigh Griffiths added a third just after the hour mark.
It was Celtic's 10th domestic win out of 10 fixtures in 2020, with 10 league games remaining as they race towards their ninth successive title for the second time in the club's history.
Steven Gerrard's Ibrox side have played a game less but the prospect of wresting the title back from the east end of Glasgow, after losing 10 points since the turn of the year, now looks remote.
Celtic skipper Scott Brown was unusually absent from the fray after picking up a calf injury in the 1-1 Europa League draw at FC Copenhagen on Thursday night – Callum McGregor took the armband – and Lennon made four changes with Simunovic, Greg Taylor, Tom Rogic, and Griffiths all coming back.
After a couple of early scares Celtic fell behind when Simunovic tangled with Brophy inside the box as they fought for a Niko Hamalainen pass, with referee Clancy pointing to the spot with no hesitation.
Celtic keeper Fraser Forster had saved his fourth penalty in seven in Copenhagen but Brophy hammered the ball past the Southampton loanee for his sixth goal of the month.
Almost at the same time, news of St Johnstone's second goal came through to cheers from home fans who rejoiced again when the full-time whistle went at McDiarmid Park.
In between events elsewhere, in the 15th minute, Rogic tested Killie keeper Laurentiu Branescu with a decent long-distance drive before the Juventus loanee blocked a Griffiths drive with his feet.
He then tipped Simunovic's powerful long-distance effort over the bar but from another corner moments later, Christopher Jullien cut the ball back for defensive partner Ajer to slam in from six yards.
Edouard then bundled the ball in from a couple of yards after Simunovic had headed back former Kilmarnock left-back Taylor's searching cross, Broadfoot failing to keep it out as he challenged.
The Killie keeper was again busy after the restart.
Edouard twice missed the target from 12 yards before the visitors were reduced to 10 men for Power's tackle on Frimpong and Alex Dyer's side struggled further.
Griffiths tapped in a Ryan Christie cut-back and he had the ball in the net again in the 72nd minute only to see the offside flag up before he was thwarted by a brilliant save from Branescu, who also parried a Taylor drive as the Rugby Park men worked hard to prevent a real thrashing.