Henrik Larsson put his midweek penalty misery behind him as the champions remained on the tails of Rangers with a comfortable victory over Jim Jefferies' men at Parkhead today.
The prolific Swedish international failed to score from the spot on Thursday as Celtic were held to a 1-1 draw by Boavista in the semi-final first leg of the UEFA Cup.
But the undaunted striker bagged his 38th goal of the campaign to set up today's victory - secured by Stilian Petrov's goal - to end a worrying run of five matches with just one win.
The triumph saw them stay eight points behind their arch rivals at the top of the Scottish Premier League with two games in hand and a game at Ibrox to look forward to.
Martin O'Neill certainly showed that his mind was fixed on retaining the championship as he named an unchanged side from that on show during the week.
That meant that Neil Lennon stayed in the side after being booed for passing the ball back against the Portuguese outfit, which was alluded to by the manager in the programme.
The home fans responded to O'Neill's outburst by chanting the midfielder's name from the start and greeting his first tackle with applause.
His team-mates were also upbeat and Alan Thompson fired just wide from 18 yards with a powerful right-foot shot from Larsson's pass in the eighth minute.
The midfielder again went close three minutes later when his left-foot effort, from the edge of the box, was pushed over the bar by Gordon Marshall.
But despite their lack of possession, Kilmarnock gave the home side a warning in the 14th minute when Gary McDonald fired over after good work from Peter Canero.
But the home side went ahead in the 20th minute courtesy of Larsson.
John Hartson controlled Thompson's cross-field pass and centred for the Swede to fire into the net from 17 yards with Marshall well out of his goal.
Celtic were looking to build on their advantage and Gary Locke had to pull Didier Agathe down to stop him getting away down the right flank.
Chris Innes then deflected Petrov's goal-bound effort from inside the box over before Hartson flicked Thompson's cross just past the post.
Larsson was then just inches away from making it two when Marshall had parried Agathe's volley into the six-yard box, but the Swede just could not get on the end of it.
A minute later and Agathe fired over from nine yards after Bobo Balde had got on the end of Petrov's corner.
Kilmarnock were hanging on and Greg Shields had to deflect Larsson's effort wide before Marshall made a good save from Hartson's header.
But Celtic should have had a penalty in the 38th minute when Agathe was clearly bundled to the ground by a clumsy challenge from Steve Fulton.
Kilmarnock seemed stunned by that decision as they let Hartson go clean through from Joos Valgaeren's header.
But the Welshman elected to go himself and Marshall saved with Larsson on his own in the centre.
Kilmarnock were hanging on after the break and they had McDonald booked for a reckless challenge on Thompson in the 48th minute.
The youngster was forced to hobble off moments later and manager Jim Jefferies decided to throw Barry McLaughlin on in his place before Lennon was booked for dissent.
Celtic were looking to kill the game off, but Marshall saved Larsson's awkward shot from Agathe's cross before the Swede fired over moments later.
Canero was the next player to be shown the yellow card after persistent fouling before the home side came agonisingly close to doubling their lead.
Lennon played a great ball down the flank to Paul Lambert and the Scotland international crossed to Larsson, whose shot flew just past the upright.
Thompson was equally as close in the 65th minute when his left-foot shot went inches past the post before Hartson blazed wide moments later.
But the home side secured the points in the 73rd minute when Petrov fired home following their best move of the game.
Larsson placed the ball into his path after good work from Hartson down the right wing and the Bulgarian international blasted a low show past the despairing dive of Marshall.
Valgaeren could have increased Celtic's advantage in the 76th minute after exchanging passes with Larsson inside the box, but his shot was saved by the Kilmarnock goalkeeper before the striker headed the rebound over the crossbar.
Celtic failed to get any more goals, but Larsson managed to banish Thursday's agony as the home side kept the pressure on their arch rivals at the top of the SPL table.