With Rangers' win on Saturday having ruined any chance of a title party at Parkhead the home side looked a bit flat in the first half against a St Johnstone side who had won on their last visit.
The visitors came close with headers from Cillian Sheridan and Francisco Sandaza before two goals in three second-half minutes claimed three points for Celtic.
Georgios Samaras headed the first past Alan Mannus from a Kris Commons free-kick before Chris Millar turned the Greek striker's cross past his own keeper as Celtic got back to winning ways after back-to-back defeats.
The Hoops, who are 18 points clear with six games remaining, now only need a point from next Saturday's match away to Kilmarnock to clinch their first SPL championship in four years.
At Celtic Park, the home side brought in Glenn Loovens and Mikael Lustig for the suspended Cha Du-Ri and Victor Wanyama.
The first chance was carved out by Samaras who showed great ball juggling skills in the box before laying the ball off to Anthony Stokes whose header went straight to the keeper.
Jody Morris fired wide for St Johnstone after good work by Sandaza down the left wing before Commons sent a snapshot over the bar at the other end.
Stokes then played a perfectly weighted pass to Commons in the box but the Scotland international pulled his angled drive wide of the post.
Liam Craig tested Fraser Forster with a curling free-kick from 25 yards before Frazer Wright cleared Charlie Mulgrew's effort off the line after he got on the end of a Commons free-kick.
St Johnstone could have taken the lead three minutes after the break when Dave MacKay's cross was met by Sheridan but the Irish striker couldn't direct his header on target.
Sandaza then sent a looping header on to the roof of the net from Craig's free-kick as St Johnstone continued to threaten.
The Hoops looked out of ideas going forward before Samaras gave them a 66th minute lead when the Greek striker rose to met a Commons free-kick and direct a downward header past Alan Mannus.
Just over three minutes later Celtic made sure of the three points when they made it 2-0 in a sweeping counter-attack move. Samaras raced down the right wing and sent in a fiercely struck delivery looking for Gary Hooper but Millar's attempted clearance flew past his own keeper.
Forster had to scramble to tip a Craig free-kick over the bar before the midfielder blazed a shot over with the goal gapping as St Johnstone couldn't find a way back into the game.
Source: AFP
Source: AFP