Following a frantic start, the first real opportunity of the match fell to the in-form Griffiths but the Hoops striker arrowed his shot narrowly wide.
Aberdeen responded with Rooney flicking a Niall McGinn cross from the right inches over the bar.
The Dons striker looked in the mood and minutes later dinked a Jonny Hayes delivery onto the roof of the net.
Aberdeen had the ball in the net in the 24th minute when Rooney stabbed home a cross from close range but the visiting fans' joy was short-lived as it was immediately ruled out for offside.
Some superb goalkeeping from the SPFL's best goalkeeper Danny Ward kept the game goalless four minutes later when he rushed off his line and produced a magnificent reflex save to keep Griffiths' effort out.
A golden opportunity to take the lead was wasted by Rooney way in the 35th minute with Hayes once again swinging a vicious delivery into the box but the striker's header from right in front of the goal went wide.
Kenny McLean then came to Aberdeen's rescue at the other end as he headed Dedryck Boyata's looping header onto the underside of the bar.
The deadlock was finally broken in the 44th minute through Griffiths.
The Scotland striker ghosted in between Taylor and substitute Paul Quinn to get on the end of a deep delivery into the box from Kieran Tierney and bullet a header beyond Ward.
The chances kept coming in the second half with a shot from Australian international Tom Rogic stinging the palms of Ward before Commons sent an effort on the half-volley wide.
A ludicrous challenge from Taylor then saw Celtic awarded a penalty. The defender scythed down Commons on the far left-hand edge of the box and Griffiths expertly dispatched his spot-kick beyond Ward.
A fantastic finish from Forrest made it 3-0. The impressive Rogic drove at the retreating Aberdeen defence before threading the ball through to Forrest who took a touch before prodding past Ward.
Substitute Peter Pawlett then had his header stopped on the line before Rooney headed Hayes' cross past Craig Gordon to reduce the deficit late on.
Source: Yahoo Sports