Having had a tricky start to their league campaign, the defending champions managed to climb above Hearts in the division.
The game itself required the 'Bhoys' to fight hard against a resilient Livingston side who have been impressing so far this campaign.
Celtic had the majority of the ball during the game and had an incredible 17 shots, with only six going on target, to their opponents' seven.
Even though the former Liverpool boss will undoubtedly think they his side should have got the three points, their ascent to the top of the table, with a game in hand, confirms an impressive turnaround in their performances of late.