A double from Norwich City target Gary Hooper along with goals from Georgios Samaras and Lassad Niouoi strike helped Celtic comfortably past Hearts.
The Glasgow side did suffer a scare after Jason Holt's deflected strike got the Tynecastle side back into the game, but the home side never looked like losing their lead.
Celtic made a total of four changes from the side that defeated Motherwell before the winter break, with goalkeeper Fraser Forster injured, Kelvin Wilson suspended and Beram Kayal dropped to the bench, while Efe Ambrose is at the African Cup of Nations with Nigeria, with Lukasz Zaluska, Mikael Lustig, Scott Brown and Joe Ledley all coming in.
John McGlynn brought in on-loan Liverpool defender Danny Wilson, along with Andy Webster, Callum Paterson and Holt, in place of skipper Marius Zaliukas and Ryan Stevenson who were both suspended, while Scott Robinson missed out with injury and Arvydas Novikovas dropped to the bench from the side that drew the Edinburgh derby at home to Hibernian.
Within 90 seconds of the game starting the visitors found themselves a goal down as Hooper continued his torment of the Tynecastle side, getting on the end of a cross from the right of the penalty area by Adam Matthews that allowed the English striker to tap home from close range.
The SPL leaders continued to pile on the pressure and claimed a second goal when Kris Commons waltzed past Kevin McHattie before racing past Wilson; his strike was parried by Jamie MacDonald into the path of Samaras, who had the simplest of tasks to double Celtic's lead.
Neil Lennon's side continued to go forward and could have added a third as Victor Wanyama got on the end of an Adam Matthews corner at the back post. The Kenyan midfielder then rifled the ball back into the danger area, but Charlie Mulgrew could not divert it on target.
Celtic thought they had claimed a third in the second half when Hooper got onto the end of a Samaras cross, knocking the ball into the net, but unfortunately for the Norwich target he was flagged offside.
It should have been three for Celtic after some wonderful work from Samaras on the left saw him cross into the box for Hooper, who laid the ball off to Ledley, but MacDonald pulled off a superb save.
Hearts did manage to get one back as Holt raced through the middle of the park, bursting into the box and his strike towards goal smacked off of Mulgrew and past Zaluska in the Celtic goal.
The victory was secured for Lennon’s side late on as Brown raced down the right wing and played the ball into the box for Hooper, who stroked it beyond MacDonald for his second of the game.
As the game entered injury time substitute Lassad put the icing on the cake getting in at the back post to an Emilio Izaguirre cross, to finish off the scoring.