Celtic strolled to their 25th consecutive league victory and also had the satisfaction of extending their lead at the top to a near impregnable 16 points as closest rivals Rangers slipped up at Tannadice.
With important UEFA and Scottish Cup games coming up Celtic were able to rest Henrik Larsson and Chris Sutton with almost 25 minutes remaining, such was their dominance.
Yet Livingston did have their chances especially in the first half when Derek Lilley should have done better than only score once.
However Celtic snuffed out the visitors' challenge with two quick goals after the break before coasting to the final whistle.
Livingston had the first chance of the game when a Marvin Andrews ball back across goal found Lilley, but Robert Douglas did well to touch over the striker's header.
This escape seemed to rouse Celtic and they took the lead shortly after. Stanislav Varga played a one-two with Sutton before crossing to leave Stephen Pearson with a simple tap in.
Lilley then passed up a marvellous chance to equalise when Lee Makel found him clear in front of goal but somehow Douglas got over to block his shot.
There was nearly a bizarre own goal by Livingston skipper Stuart Lovell when keeper Roddy McKenzie was just able to avert his over strong pass back for a corner.
Larsson volleyed home from close range but his effort was disallowed because of a foul by Bobo Balde on the keeper.
Celtic's second was not long delayed as Sutton stretched out a long leg to toe poke home a ball which McKenzie should have claimed as it spun high into the air after Alan Thompson's free-kick.
Livingston stunned the home crowd when they pulled a goal back just before half time. Slack defending in the Celtic rearguard allowed Burton O'Brien time to find Lilley in acres of space and the striker's shot finally found the net.
Thompson restored the Bhoys' two-goal advantage early in the second half when he cleverly curled his shot past the keeper after Sutton had done well to create the chance.
When McKenzie collected a pass back under pressure from Larsson it was all over for the visitors as the striker curled his shot from the indirect free-kick past the massed ranks of Livingston players.
McKenzie saved well from Neil Lennon before Andrews pulled down substitute Craig Beattie on the edge of the box.
Thompson delicately chipped home the spot-kick to leave Livingston happy to hear the final whistle without suffering any more damage.