Match ends, Celtic 3, Kilmarnock 1.
Celtic recovered from losing an early Kilmarnock goal to win handsomely and march 12 points clear at the top of the Scottish Premiership.
With Rangers drawing at St Johnstone, Neil Lennon's men took advantage as they bid to win a ninth title in a row.
Eamonn Brophy's penalty had initially rocked Celtic but Kristoffer Ajer and Odsonne Edouard had the hosts ahead.
Leigh Griffiths added a third shortly after Kilmarnock were reduced to 10 men following Alan Power's second yellow.
The champions have now won 15 of their last 16 home games, with 32 goals scored since the winter break.
For Kilmarnock it was a third defeat in a row and leaves them five points off a place in the top six.
Are Celtic now unstoppable?
Celtic did what champions do. They had the opportunity to extend their lead in the table and continued their relentless and now seemingly inevitable march to the title.
That happened despite an early setback. Kilmarnock started brightly and forced early corners with Nicke Kabamba going close but his shot was blocked. However, their persistence paid off.
Jozo Simunovic dived in rashly but didn't win the ball cleanly. His attempts to recover resulted in Brophy being impeded inside the area and the Scotland forward tucked away the spot-kick impressively.
As that goal went in, St Johnstone scored against Rangers in Perth to ease the pain for Celtic fans - and soon things got even better.
Alex Dyer's side dropped very deep and ultimately could not hold out. They had no out ball and Celtic forced the issue.
Griffiths was denied after superb build up by Edouard. Simunovic then sent in a deflected effort that was tipped over by Laurentiu Branescu.
Any resistance appeared unlikely to last and was pierced when Christopher Jullien scrambled the ball back into danger from a corner and Ajer bundled home.
Kilmarnock's approach increasingly allowed Celtic defenders to step out as they had little to contend with. It proved key as Simunovic nodded Greg Taylor's cross back to Edouard, who outmuscled Kirk Broadfoot to net the second.
The second half was a procession towards Kilmarnock's goal as Celtic searched for the crucial third.
That task became more straightforward when Power received a second yellow after tackling Jeremie Frimpong. It seemed rather harsh as the young Celtic wing-back seemed to have lost control of the ball.
Unsurprisingly, the third goal arrived. An incisive move down the left released Ryan Christie to the bye-line and he pulled the ball across for Griffiths to tap home.
Brilliant play looked to have created a fourth but Griffiths's strike was ruled offside, before he was then superbly denied by Branescu as time ticked on.
Celtic are flying and with a 12-point lead in the title race it feels like a huge task for Rangers to reel them in from here.
Man of the match - Odsonne Edouard
The young French striker is a class act and seems to thrive alongside Griffiths. Celtic fans will be desperate to retain him beyond the summer as he has everything.
His goal return is strong but it's Edouard's ability to be calm, to bring others into play that's equally impressive. He is strong, always in full control of the ball, and more often than not picks the right option. He is an absolute nightmare for any defender and when you consider his youth, he has room to get better.
He netted again today and produced another impressive display that went a long way to delivering another league win.
'I thought we were outstanding' - reaction
Celtic manager Neil Lennon: "I thought Eamonn [Brophy] was offside, but our reaction to that was fantastic. It was a real magnificent performance. I thought we were outstanding.
"To be fair to Alex Dyer, he went with two strikers. But we dealt with that very well. I said to the players 'don't think it's easy what you're doing'. It's important we keep the momentum going."
Kilmarnock manager Alex Dyer: "We were doing alright - I thought we were in control. Then they started to play a bit, put us under pressure. We were sloppy for the goals, and scored maybe too early.
"The gameplan was to win the game, or at least get a point, but we came up against a side in really good form. I'm still happy with my boys - they worked hard and gave it all they've got after a hard week."
- 18RogicSubstituted forElyounoussiat 74'minutes
- 42McGregorBooked at 67mins
- 9GriffithsSubstituted forBittonat 82'minutes
- 22EdouardSubstituted forBayoat 74'minutes
- 26Del FabroSubstituted forTaylorat 71'minutes
- 15El MakriniBooked at 21minsSubstituted forBurkeat 45'minutes
- 6PowerBooked at 57mins
- 9BrophySubstituted forKiltieat 65'minutes
- Kevin Clancy
- Shots on Target
Second Half ends, Celtic 3, Kilmarnock 1.
Mohamed Elyounoussi (Celtic) wins a free kick in the attacking half.
Foul by Kirk Broadfoot (Kilmarnock).
Attempt saved. Greg Taylor (Celtic) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Callum McGregor.
Attempt blocked. Nir Bitton (Celtic) right footed shot from outside the box is blocked. Assisted by Kristoffer Ajer.
Hand ball by Gary Dicker (Kilmarnock).
Foul by Mohamed Elyounoussi (Celtic).
Kirk Broadfoot (Kilmarnock) wins a free kick in the defensive half.
Substitution, Celtic. Nir Bitton replaces Leigh Griffiths.
Attempt missed. Ryan Christie (Celtic) left footed shot from outside the box is too high. Assisted by Jeremie Frimpong.
Corner, Celtic. Conceded by Laurentiu Branescu.
Attempt saved. Leigh Griffiths (Celtic) left footed shot from the centre of the box is saved in the top left corner. Assisted by Jozo Simunovic with a cross.
Attempt missed. Vakoun Issouf Bayo (Celtic) header from the centre of the box misses to the left. Assisted by Jeremie Frimpong with a cross.
Attempt missed. Greg Kiltie (Kilmarnock) right footed shot from outside the box is high and wide to the right. Assisted by Niko Hämäläinen.
Substitution, Celtic. Mohamed Elyounoussi replaces Tomas Rogic.
Substitution, Celtic. Vakoun Issouf Bayo replaces Odsonne Edouard.
Offside, Celtic. Ryan Christie tries a through ball, but Greg Taylor is caught offside.
Substitution, Kilmarnock. Ally Taylor replaces Dario Del Fabro.
Attempt saved. Tomas Rogic (Celtic) right footed shot from the centre of the box is saved in the centre of the goal.