After a first half in which Gordon Strachan's men looked unsettled and failed to find the back of the net, Maciej Zurawski and Shaun Maloney both scored early in the second half to secure the points and restore the Hoops' 17-point lead at the top of the table.
It was Livingston who made the better start with David McNamee's dangerous cross forcing Stephen McManus to head narrowly over his own bar after just a few seconds of play.
At the other end Zurawski was making his presence felt when he broke clear of his marker and sent an eight-yard shot just over the crossbar.
It was end-to-end play and Richard Brittain produced another chance for Livi, forcing a reflex save from Artur Boruc.
Dion Dublin produced a half-chance for Celtic before Sam Morrow clattered a shot off the crossbar for Livi.
But despite Livingston's notoriously leaky defence, Celtic couldn't break it down and finished the first half frustrated at their inability to take control of the match.
It was a different story in the second half as it took the champions-elect less than two minutes to make their mark on the scoresheet through Zurawski.
Five minutes later it was 2-0 when Dublin was tugged down in the area by Greg Strong and Maloney stepped up to convert the resulting penalty.
After two quick goals Celtic seemed content to sit on their advantage and produced little in the way of scoring opportunities until the last five minutes of the game, when both Stilian Petrov and Maloney had good chances which they failed to convert.
A win in their next match - a midweek clash against second-place Hearts - will be enough to officially seal the championship for Celtic, while Livingston look to be firm favourites for relegation, languishing nine points off the pace at the bottom of the table.