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Goals from Scott Sinclair and James Forrest in the second half extended Celtic’s lead at the top of the table to 26 points and extended their unbeaten domestic run to 39 games.
The away side set up with a back six in the first-half leaving little room for Celtic to exploit and making it difficult to break them down.
As a result Stuart Armstrong lashed a shot from distance into the bottom left corner to open the scoring after 22 minutes for his 14th goal of the season.
On 48 minutes Patrick Roberts lifted a deft ball to Scott Sinclair at the back post but the in form winger couldn’t hit the target.
Against the run of play, Kilmarnock equalised on 65 minutes after Jordan Jones’ deflected shot redirected beyond the clutches of Craig Gordon and into the net.
Six minutes later Sinclair put Celtic ahead again from close range and on 76 minutes James Forrest made it three with a header from close range.
Here are the player ratings for today’s game.