Against the run of play, Kilmarnock took the lead on 32 minutes following a stunning 40-yard strike from Souleymane Coulibaly.
Within three minutes Celtic equalised through Dembele after being picked out inside the box by Mikael Lustig and fired the ball into the right-hand corner.
Dembele was on target once again on 38 minutes after the Hoops’ other full-back, Kieran Tierney got down the left wing and cut the ball back to the Frenchman who lashed home his 10th goal of the season into the top left corner.
On 52 minutes Forrest made it three after linking up with Rogic on the edge of the box and ran past two Kilmarnock players before scoring.
Griffiths came off the bench and made it four after getting the final touch on Scott Sinclair’s corner on 66 minutes.
Five minutes later the striker won a penalty and unselfishly gave the ball to Sinclair who scored in his sixth consecutive game from the penalty spot.
Rogic made it six from the edge of the box with five minutes remaining after the ‘keeper failed to keep out his shot.
Here are the player ratings from today’s game.
Dorus de Vries 5/10
Could do little about Coulibaly’s stunning strike from 40-yards and caught him and everyone in the ground off guard.
Mikael Lustig 7/10
Played well down the right hand side and got forward well to support Forrest. Good cross into Dembele who equalised just before half-time.
Jozo Simunovic 7/10
Gave away a silly foul early on. Comfortable in possession and moved the ball on quickly and accurately from defence to the wings to start attacks.
Erik Sviatchenko 6.5/10
Comfortable and untroubled in defence, the last man in defence as Simunovic took the ball out from the back.
Kieran Tierney 8.5/10
Bombed down the left wing continuously with great success once again and is becoming a real attacking threat for Celtic this season. Smartly pulled back a cross to find Sinclair in space and did the same minutes later to find Brown following some good link-up play with the skipper. Assisted Dembele with a trademark cutback. Awarded Man of the Match.
Scott Brown 7.5/10
First to the second ball to keep possession for Celtic and maintain their early dominance deep inside Kilmarnock’s half. Had two efforts on goal, the second of which he should have at least got on target from Tierney’s cutback. Good ball down the line to Tierney which led to the second goal.
Nir Bitton 7/10
Closed the ball down well high up the field to pin Kilmarnock in and win back possession. Good switch of play to Tierney several times who was in space on the left wing.
James Forrest 7.5/10
Curled a shot from a good position inside the box over the bar. Good link up play with Rogic and ran past two Kilmarnock players before poking the ball home for the third goal.
Tom Rogic 8/10
Had an early shot on the edge of the area blocked. Great run forward at the defence and a good through ball to find Dembele. Good through ball to Forrest for the third. Another good game using his pace and strength to get past players and bring others into play. Got his goal with five minutes remaining after the ‘keeper made an error and let it through his finger tips.
Scott Sinclair 7/10
Fired a shot over the bar early on. Had another chance inside the box that was terrifically blocked. Turned a defender on the edge of the box but hit his shot straight at the ‘keeper. Didn’t have the best game but got his goal from the penalty spot.
Moussa Dembele 8/10
Fired a shot over the bar after winning back possession just outside the box. Equalised from Lustig’s cross minutes after Kilmarnock scored with a strong side footed effort. Scored again two minutes later from Tierney’s cross. Could have got his perfect hat-trick but headed just over the bar.
Craig Gordon 6/10
Had little to do in the second half as Celtic dominated.
Leigh Griffiths 7/10
Came off the bench and got the final touch on Sinclair’s corner for his eighth goal of the season. Unselfishly gave the ball to Sinclair after winning a penalty.
Patrick Roberts 6/10
Came on for Scott Sinclair on 73 minutes after he got his goal. Looked much sharper than he did in midweek as Celtic played with confidence and swagger when he came on.