Brendan Rogers' team are wanting to win their eighth consecutive Scottish league title this season, and made a perfect start in their attempt to do that.
The Glasgow team took the lead after just 8 minutes after Australian forward Tom Rogic scored with a header from a cross from winger Jonny Hayes.
They doubled their lead on 26 minutes after French striker Odsonne Edouard stabbed home after a mis-hit shot from his compatriot Olivier Ntcham, before Ntcham scored a penalty on 50 minutes to make the scoreline 3-0.
In the dying moments of the game, Livingston got a consolation goal through Scott Robinson to take the clean sheet away from Craig Gordon.
Rogers' team dominated the game after enjoying 68% posession and having 21 shots on goal, but are not top of the table due to rivals Hearts having a superior goal difference after their 4-1 win over Hamilton Academical.