Goalkeeper Artur Boruc withdrew at the last moment, but substitute keeper Mark Brown did not even have one save to make throughout the 90 minutes.
Celtic were deservedly two up within the opening half-hour with Jan Vennegoor of Hesselink and Aiden McGeady finding the net.
Scott Brown served up a magnificent display of midfield play and set up Scott McDonald for Celtic's third just after the break.
The home team were on the front foot from the start and Alexander Diamond did well to head clear McGeady's cross.
It was all one-way traffic towards the Aberdeen goal and McGeady's snap-shot nearly deceived Jamie Langfield at his near post.
The visitors had a half-chance when Scott Severin's free-kick fell to Lee Mair but he pulled his shot wide.
A swift break between Brown and McGeady ended with Diamond producing another superb tackle as Vennegoor of Hesselink was poised to shoot.
Aberdeen paid the penalty when they failed to clear their lines. Brown crossed the ball back in and Jiri Jarosik's header was glanced home by Vennegoor of Hesselink.
Celtic continued to threaten with Langfield parrying away powerful shots from McDonald and Brown before watching in relief as Jiri Jarosik's 30-yard strike clipped the top of the bar.
The home team added to their lead when McGeady cut inside Richie Byrne before unleashing a superb left-foot shot which left Langfield helpless.
Aberdeen threatened briefly before the interval but Lee Miller pulled his shot wide.
McDonald then put the result beyond doubt just after the break after a shocking blunder by Langfield.
Brown raced past Severin before passing to McDonald, whose shot appeared to be held by the keeper but somehow Langfield fumbled the ball allowing McDonald to shoot into the empty net.
Jarosik headed wide from six yards with the goal gaping, while Miller did have the ball in the net for Aberdeen but was clearly offside.
Langfield then produced a marvellous double save to deny McGeady and Vennegoor of Hesselink, but after this result there is no doubt who will be approaching their European tie next week in a better frame of mind.