A Henrik Larsson double sent the Scottish champions back to the top of the pack at Almondvale today - but an injury to Stilian Petrov may have dealt Martin O'Neill a major European injury scare.
In the build up to the first goal, influential midfielder Petrov was forced off to have 12 stitches in a facial wound after colliding with Marvin Andrews.
That presented O'Neill with an unwelcome distraction just four days before his side face Spanish side Celta Vigo in the UEFA Cup third round at Parkhead.
Larsson struck from the spot early in the first-half and late on to take his season's tally to 24 and move Celtic a point clear of Rangers again.
Celtic made the perfect start when they took the lead after just four minutes.
The striker threaded the ball through to Petrov, who centred for Paul Lambert to fire into the back of the net.
Confusion ensued before referee Stuart Dougal pointed to the spot for a foul on Petrov and Larsson sent Javier-Sanchez Broto the wrong way from 12 yards.
The visitors should have gone further ahead in the 16th minute when Momo Sylla found Larsson on the right and he put his versatile team-mate clean through on goal, but Broto was quickly off his line to make a crucial one-handed save to deny him.
Broto again kept the home side in the game in the 20th minute when Alan Thompson found Larsson, who turned superbly and unleashed a powerful drive which the Spanish goalkeeper did well to turn away.
Sylla also went close again a minute later as Larsson flicked the ball into his path and the winger blazed his right-foot just wide from a tight angle.
Livingston's frustration started to boil over and Gustave Bahoken was then booked for a late challenge on Sutton, who was also booked for dissent.
Leishman and Hay must have vented some of their anger at the players in the dressing room during the interval as his team finally started to cause Celtic problems at the restart.
The home side began to pass the ball better and show more composure and the unmarked Rubio could have got his side level in the 48th minute when he got on the end of Wilson's corner, but he headed high over the bar.
Celtic however, should have killed the game off in the 62nd minute when Larsson got the better of Bollan from Neil Lennon's ball over the top and he pulled the ball across to Sylla, who failed to control the ball and the chance went begging.
Encouraged, the home side continued to threaten and Celtic keeper Robert Douglas was relieved to see Bollan's swirling 25-yard free-kick sail just over his crossbar.
Livingston came even closer to an equaliser in the 78th minute when Andrews saw his header from Rolando Zarate come back off the crossbar from just six yards.
But Larsson eased Celtic's fears with eight minutes remaining when Oscar Rubio slipped and he cut inside to strike the ball past Broto.
The Swede's late goal ensured that there were no worries in the final moments - but Petrov's injury will be a big concern for O'Neill in the next few days.