Stephen Pearson opened his account for Celtic as they eased to victory and stretched their run of consecutive league wins to 20 games.
Stephen Pearson celebrates his first goal for Celtic
The recent signing from Motherwell scored for the league leaders 13 minutes into the second half.
Stilian Petrov and Henrik Larsson had already put Celtic in command before the break despite some good early play from the hosts at Pittodrie.
Aberdeen did hit back through Steve Tosh, but it was a mere consolation.
Dons boss Steve Paterson had been forced into changes following injury to experienced pair Russell Anderson and Scott Booth.
Phil McGuire came into defence, David Zdrilic was up front, while Scott Muirhead came in as former Celtic striker Bryan Prunty dropped to the bench.
Bobo Balde's participation in the African Cup of Nations with Guinea allowed young John Kennedy a rare start for Celtic.
Second-bottom Aberdeen made a bright start in the early afternoon winter sunshine, but it was Celtic who created the better early chances.
A header from Larsson, whose goal confirmed his place as the third top scorer in Celtic's history, bounced back off a defender into the striker's path, but he pushed his volley wide from 10 yards.
John Hartson was denied an opener when David Preece clawed the Welsh striker's header from eight yards off the goal-line at his left-hand post.
Aberdeen were finding it hard to create clear-cut chances, but goalkeeper Rab Douglas was at least forced into action to hold a low shot on the turn from Zdrilic.
Henrik Larsson (left) scored Celtic's second goal
Celtic almost grabbed themselves a bizarre opener when a clearance from Zander Diamond struck Larsson and came off the crossbar.
The breakthrough came after 30 minutes, Larsson chesting the ball into the path of Petrov, whose low drive from the edge of the box went in off the post.
Aberdeen attempted to strike back immediately and Douglas did well to turn a 16-yard Chris Clark volley round the post.
Celtic were well on their way to victory a couple of minutes before the break, when a Jackie McNamara cross to the back post found Larsson unmarked and he volleyed the ball past the despairing Preece.
The game was effectively killed off as a contest after 58 minutes, when a Larsson shot was deflected over the head of the goalkeeper and Pearson stole in at the back post to score.
Aberdeen grabbed a goal back four minutes later, a Zdrilic shot being deflected into the path of Tosh, whose shot on the turn slipped under the diving Douglas.
Aberdeen: Preece, McNaughton, McGuire, Diamond, Morrison, Clark, Tosh, Heikkinen, Muirhead, Zdrilic, Hinds.
Subs: Esson, Sheerin, Rutkiewicz, Foster, Prunty.
Celtic: Douglas, Varga, Kennedy, McNamara, Agathe, Lennon, Sutton, Petrov, Pearson, Hartson, Larsson.
Subs: Hedman, Sylla,
Valgaeren, Lambert, Maloney.
Referee: J Rowbotham (Scotland).