Kenny Miller came off the bench to grab the winner as Celtic came from behind to edge out Kilmarnock and stretch their lead in the SPL to 10 points.
Kenny Miller scored four minutes after coming on as a substitute
Killie's Steven Naismith came closest to scoring during an even first half when he hit the bar with a volley.
Sub Colin Nish scored for the hosts with a low drive just before the break.
But, six minutes later, Shunsuke Nakamura curled in a free-kick and, with 15 minutes to go, Miller secured all three points from close range.
Miller and Evander Sno had started on the bench with the midweek Champions League game against Benfica in mind.
And it was the men who replaced them in the starting line-up, Jiri Jarosik and Stephen Pearson, who combined to make the game's first chance - Pearson dragging his shot wide from 12 yards out.
Pearson drove another shot wide and Maciej Zurawski forced a save from Graeme Smith with an effort from 18 yards.
But Kilmarnock, who were without injured striker Gary Wales, were giving as good as they got in a game in which defences were on top and almost snatched the lead just before the break.
Garry Hay's cross found Naismith 12 yards from goal, but the striker's volley crashed off the crossbar.
Kilmarnock claims for a penalty were waved away moments later after a Shaun Maloney tackle on James Fowler.
Colin Nish (right) put Killie into the lead at Rugby Park
And the home side's chances appeared to suffer a blow when David Fernandez, who had been tormenting his former club, had to be stretchered off following a late Gary Caldwell tackle.
The Spaniard was replaced with Nish and the former Dunfermline striker made an almost instant impact four minutes after the restart.
Zurawski had already squandered a chance when a Lee Naylor cross evaded Frazer Wright, but the Polish striker headed wide from 10 yards.
Nish then won the ball from Nakamura in midfield and made room for himself to collect a neat return pass from Wales' replacement, Leven, before driving it home from 16 yards.
Celtic responded immediately, a Maloney drive from the edge of the box shaving the outside of the post.
And Nakamura did even better, curling a superb free-kick into the far corner of the net from 25 yards.
Celtic began to dominate and, within four minutes of replacing Zurawski, Miller stole in unmarked to bundle home a low Maloney cross to the far post.
A Nish header that looped on to the top of the net was the closest that Kilmarnock came to rescuing what would have perhaps been a deserved point and their unbeaten home record.
Kilmarnock: Smith, Greer, Hay, Grant Murray, Frazer Wright, Fowler, Johnston, Leven (Stephen Murray 79), Invincibile, Naismith (Dodds 89), Fernandez (Nish 45).
Subs Not Used: Combe, Lilley, O'Leary, Adams.
Booked: Frazer Wright.
Goal: Nish 49.
Celtic: Boruc, Telfer, Naylor, McManus, Caldwell, Lennon, Pearson, Nakamura (Sno 88), Jarosik (McGeady 46), Maloney, Zurawski (Miller 70).
Subs Not Used: Marshall, O'Dea, Riordan, Balde.
Booked: Caldwell, Boruc.
Goals: Nakamura 55, Miller 75.
Ref: J Underhill