Stilian Petrov, Shaun Maloney and Maciej Zurawski scored in the second half as Celtic extended their lead at the top of the Bank of Scotland Premier League to 16 points over second-placed Hearts.
An outstanding first-half performance by Aberdeen goalkeeper Jamie Langfield had kept the home side at bay, but there was an inevitability about the breakthrough after the restart.
Bulgarian international Petrov netted the opener after 66 minutes, slamming a Zurawski cut-back into the roof of the net to ease the tension inside Parkhead.
The impressive Maloney capitalised on some hapless defending 10 minutes later to make it 2-0, before Zurawski scored Celtic's third a minute from time to highlight the true difference between the two sides.
It was a comfortable victory in the end but Aberdeen might have achieved better with even a modicum of belief, as Celtic looked nervy at times when the match was goalless.
The game kicked off against a backdrop of friction between the two clubs.
Aberdeen's request to have the match postponed because weather conditions in the north east of Scotland made it difficult for their fans to travel was rebuffed by the Scottish Premier League, and Hoops manager Gordon Strachan, a former Dons player, had shown little sympathy for the plight of his former club.
On the pitch it was the home side who took the initiative.
In the 10th minute Petrov sent Zurawski through on goal but the Pole's left-footed drive from 16 yards, under pressure from Dons stopper Alexander Diamond, was saved by Langfield at the second attempt.
Then a clever pass at the edge of the Aberdeen penalty area from Celtic midfielder Maloney gave Roy Keane an opportunity to get his angled shot in from close range, but again Langfield was up to the task.
In the 18th minute the Dons goalkeeper pulled off yet another good block, this time from Petrov's
close-range volley following Paul Telfer's cross into the six-yard box.
Celtic were denied what looked like a good penalty claim moments later when Maloney's attempted cross to Zurawski from the left appeared to hit the hand of Diamond 10 yards from goal, but referee Mike McCurry waved play on.
In the 27th minute, Keane's left-footed shot was saved by Langfield seconds before the former Dundee goalkeeper made an even better block from the unmarked John Hartson's drive from eight yards.
Just after the half-hour mark Aberdeen midfielder Barry Nicholson was taken off on a stretcher after a robust challenge by Keane to be replaced by Richard Foster.
Utility player Scott Severin, playing in attack with Steve Lovell, sent in Aberdeen's first shot on goal from distance in the 32nd minute but Hoops goalkeeper Artur Boruc saved easily.
Vocal frustration from the home support followed McCurry's whistle to end the first period.
Aberdeen looked to fancy their chances of causing a shock as the second half began.
However, the match quickly reverted back to type. Zurawski's unconvincing drive from 18 yards sailed high over the bar to relieve the pressure on Langfield's goal.
At the other end, an Aberdeen break ended with Severin failing to properly test Boruc with his left-footed drive from 16 yards.
Just after the hour mark a terrific run by Foster from the half-way line into the Celtic penalty area caused panic and was ended only by a Boruc save.
Then, at the other end, Maloney sent a 25-yard free-kick straight into the arms of Langfield.
The home side eventually broke the deadlock through Petrov.
Keane set up Zurawski wide on the right with a fine pass and when the Polish international's pass came to the Bulgarian 16 yards from goal, he hammered the ball first time into the roof of the net.
The Parkhead men, unburdened of the tension, made it 2-0 nine minutes later after some pinball in the Dons' penalty area.
Keane's cross from the right was cleared by Aberdeen defender Chris Clark only for the ball to hit Diamond and fall to the feet of Maloney who quickly whipped it into the net from close range.
In the 89th minute, as Celtic played with the Pittodrie men, Zurawski scored a third after being unselfishly set up by Petrov six yards from goal.
Teams:
Celtic Boruc, Telfer, Balde, McManus, Wilson, Petrov, Lennon,Keane, Maloney, Zurawski, Hartson (Nakamura 63).
Subs Not Used: Marshall, Varga, Pearson, Wallace, Dublin,
Lawson.
Booked: Balde.
Goals: Petrov 66, Maloney 75, Zurawski 89.
Aberdeen Langfield, MacFarlane, Anderson, Diamond, McNaughton,Nicholson (Foster 31), Severin, Griffin (Crawford 73), Clark,Lovell, Snoyl (Mackie 38).
Subs Not Used: Kelly, Dempsey, Stewart, Macauley.
Booked: MacFarlane.
Att: 60,018
Ref: M McCurry (Scotland).