Livingston 0-2 Celtic
Alan Thompson seals the points with a well-taken volley
The Celtic juggernaut showed no signs of being stopped by Livingston despite a stuffy defensive display by the home side.
Celtic were unable to break the deadlock in a first half in which they dominated proceedings, but Chris Sutton eased any nerves the visitors had with the opening goal three minutes into the second period.
Livingston rarely threatened Magnus Hedman's goal and Sutton's strike looked like being enough to take the three points.
Alan Thompson put the issue beyond doubt, however, with a fine volley five minutes from time.
Celtic made most of the early running and Jackie McNamara was first to test Livi goalkeeper Roddy McKenzie with a near-post drive, which the keeper did well to tip over the bar.
Livi were finding it difficult to keep possession in the opening minutes and Celtic almost benefited after eight minutes.
Thompson was gifted the ball, which he played into the path of Sutton who fed Henrik Larsson, but though the Swede's shot beat McKenzie, David McNamee got back well to clear off the line.
Two minutes later, Francisco Quino had Livi's first effort on goal, but his 25-yard drive rose just too high.
Larsson curled a shot wide and Bobo Balde headed just past the post, but as the half wore on, the game developed into a midfield battle with neither keeper being asked too many questions.
On the stroke of half time, Magnus Hedman was called into action for the first time when he got a fingertip to a Jamie McAllister free kick that looked to be heading just over the bar in any case.
The deadlock was broken three minutes into the second half when Thompson's chip found Sutton, who controlled the ball with his back to goal, held off the challenge of Oscar Rubio before swivelling and sweeping a left foot shot past McKenzie.
Chris Sutton celebrates the opening goal
Thompson brought a good save out of McKenzie a few minutes later when he let fly from the edge of the box, but the Livi keeper managed to turn the ball round the post.
Larsson had an effort cleared off the line for the second time in the game after 56 minutes when he managed to get goal-side of Rubio to get his shot away. McKenzie got a hand to the ball to slow its progress, allowing Emmanuel Dorado to get back to clear the danger.
Liam Miller had a powerful drive well held by McKenzie midway through the second half as Celtic looked for the killer second goal and Larsson clipped a shot just wide shortly afterwards.
With eight minutes remaining, Livi might have got an unlikely equaliser when Juanjo Camacho flicked the ball onto Fernando Pasquinelli inside the box and the striker's acrobatic scissor kick beat Hedman but flew just over the bar.
The game was ended as a contest moments later when Neil Lennon's cross was headed clear by Rubio but fell beautifully for the left foot of Thompson who smashed an unstoppable volley into McKenzie's bottom left-hand corner.
Livingston: McKenzie, Rubio, Dorado (Camacho 76), Andrews,
McNamee, Lovell (McGovern 67), O'Brien, Quino, McAllister,
Subs Not Used: Main, Scott McLaughlin, Snodgrass.
Celtic: Hedman, Varga, Balde, McNamara (Mjallby 90), Gray,
Miller, Petrov, Lennon, Thompson, Larsson, Sutton.
Subs Not Used: Marshall, Hartson, Maloney, Wallace.
Ref: H Dallas