Derek McInnes suffered his first defeat as Aberdeen manager as Celtic battled to a league win ahead of their Champions League match in Kazakhstan.
The visitors went ahead on the stroke of half-time when Dons keeper Jamie Langfield was sent off for hauling down Georgios Samaras and Kris Commons powered home from the penalty spot.
Fraser Forster saved a Niall McGinn header as Aberdeen tried to fight back.
But sub James Forrest made the points safe from a deflected cross.
The players reacted to the atmosphere generated by the 20,017 fans inside Pittodrie by beginning at a fizzing pace, with Celtic hounded endlessly by packs of enthusiastic red shirts when they advanced too far into their opponents' half.
Aberdeen, though, were not for sitting in too long and when Jonny Hayes raced towards the Celtic goal it took a crude challenge by Samaras to halt him.
However, McGinn's free-kick from 20 yards sailed helplessly over the goal of Forster, who Celtic manager Neil Lennon this week insisted is not for sale, despite interest from Benfica for the English keeper.
The game quickly became an untidy affair, with both sides surrendering possession far too often, the result of frantic play and careless passing.
While Celtic's pressing was repelled by Aberdeen, who threatened with the occasional long ball, it took Joe Ledley to produce the first shot on target, 29 minutes into the game.
From the right, he played a one-two with Celtic captain Scott Brown, picked up the ball again on the edge of the box and waltzed past Mark Reynolds before unleashing a shot that was saved by Langfield to his right.
For all the home crowd rose to Aberdeen's speedy attacks and forays down the left by Reynolds and Peter Pawlett, their sole effort on goal in the first half was a limp 20-yard free-kick by Ryan Jack that was easily collected by Forster.
With half-time looming, Samaras chased a long ball and evaded the despairing challenge of Russell Anderson and rounded Langfield but was brought down by the Dons keeper, giving referee Calum Murray an easy decision to send him off and award Celtic a penalty.
Commons blasted the ball low and down the middle, whizzing past replacement goalie Nicky Weaver for a 1-0 half-time lead.
Soon after the restart Celtic defender Charlie Mulgrew received a yellow card for a painful challenge on Anderson, to add to earlier bookings for McGinn and Matthews.
With 10 men and trailing, Aberdeen's desire to match season's 1991/92 feat of winning their first three league games looked forlorn.
Yet Hayes' perfect cross into the box on 51 minutes almost produced a leveller, with Forster making a point-blank save from McGinn's firm header.
At the other end Samaras had volleyed wide prior to McGinn's attempt and Brown should have rounded off a flowing move by Commons, who skinned Anderson on the right wing, but the skipper shot wide.
Weaver made a good block with his legs to divert Ledley's shot from goal as Celtic sought to make the points secure and, following a flurry of substitutions, the Englishman again denied the visitors when Mikael Lustig prodded Commons' piercing free-kick at goal from eight yards.
Three minutes from full-time, Forrest, on for Beram Kayal, broke clear down the left to meet Ledley's pass and his cross clipped Reynolds' foot and looped over Weaver and into the net to give Celtic a deserved three points ahead of Tuesday's match against Shakhter Karagandy in Champions League qualifying.
For the Reds, it was the first defeat in a competitive match for McInnes since he replaced Craig Brown as manager at the end of last season.
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