The Bhoys were under pressure to perform, with the Dons mounting an unlikely title challenge under Derek McInnes - but Celtic are now in cruise control at the top of the table, with a game in hand still to come.
Jason Denayer settled the nerves with a first half header to open the scoring, before Ronny Deila's men ran riot in the second half.
Leigh Griffiths, Gary Mackay-Steven and Stefan Johansen all added their names to the scoresheet after half-time to hand Deila a much needed three points.
It was just the response Norwegian Deila will have been looking for after his side were dumped out of the Europa League on Thursday after a 1-0 away defeat at Inter Milan.
With just over 48 hours of preparation time before facing Aberdeen, Celtic did superbly to muster enough energy to turn in such a display - and manager Deila told the Celtic official website after the game that he is proud of the way his side played after a 'tough' turnaround from the Inter game.
"I’m so happy for the performance and the result," said Deila. "I’m proud of the boys. It’s so hard to play so many games like we do now, and we didn’t get back to Glasgow till 3am on Friday and that’s a tough one when you’re going to play two days after."
"You could see in the first half we were struggling to get the tempo in our legs and Aberdeen were really fresh. They were offensive and pushed us back. They caused us problems. They didn’t have any clear chances but they had too many set-plays and they caused us difficulties."
"But we got the goal and got more energy into the team and in the second half I think there was only one team on the pitch and we could have won by more," he added.
Celtic can now move nine points clear with a win over St. Johnstone on Wednesday, where tired legs will once again have to be put to one side in order to try and clinch a fourth successive Scottish Premiership title.