Steven Gerrard's side had led the top flight after beating Hamilton and their Old Firm rivals' loss to Hibernian on Saturday.
Brendan Rodgers' side have been beaten three times in the league so far -- their worst record in a single campaign since the Northern Irishman took over in 2016.
Defender Anthony Ralston opened the scoring at Parkhead in his first appearance of the season after less than half an hour of play.
Ralston slotted home after a delicate through ball from forward Odsonne Edouard.
A second followed four minutes later from former Chelsea and Manchester City winger Scott Sinclair.
James Forrest was brought down by the visitors' Charles Dunne and Sinclair slotted home from the penalty spot for his third goal in the league this season.
The game was over as a contest seconds before the half-time whistle as 19-year-old Mikey Johnston netted his first competitive goal for the Bhoys after coming on for Edouard.
Elsewhere, Rangers failed to score for only the second time in 11 matches as they were held to a 0-0 draw in Edinburgh.
Gerrard's outfit had 19 shots on goal including efforts from the league's top goalscorer Alfredo Morelos and veteran Northern Ireland defender Gareth McAuley.
On Saturday, seven-time straight champions Celtic welcome Dundee looking to extend their advantage at the summit of the table before Rangers' trip to St Johnstone on Sunday.