Lassad Nouioui opened the scoring when he stroked into an empty net in the 73rd minute, having only come on for Kris Commons four minutes earlier. Charlie Mulgrew added a second against his former club three minutes later.
Despite the early kick-off, the crowds arrived in their numbers as Pittodrie basked in the lunchtime sun.
The home support were boosted by teenage winger Ryan Fraser's swift recovery from an ankle knock sustained in their 4-1 win over St Mirren last week. The only change to the side that had started that game saw Gavin Rae return in place of Clark Robertson.
Celtic, who had disappointingly drawn with St Johnstone, handed Tony Watt a start after the promising young striker came off the bench to find the net against the Saints. He replaced Venezuelan striker Miku in attack.
There were two further alterations to Neil Lennon's starting eleven, with midfielders Scott Brown and Joe Ledley missing out. Mikael Lustig and Beram Kayal took their places in the side.
As early as the second minute, Josh Magennis' strong run up the right flank for Aberdeen allowed him to slip a pass to Johnny Hayes, only for the former Inverness Caledonian Thistle winger to send his left-footed shot into the side netting.
And five minutes later, the Dons' top scorer Niall McGinn fashioned an opening with neat play on the edge of the area, but Fraser Forster was able to gather comfortably.
By and large, though, it was a scrappy opening period, with neither side taking command of the midfield, and possession being surrendered easily and cheaply by both sides.
Only a wickedly curling cross from Adam Matthews had caused any concern for Aberdeen so far, although that drifted harmlessly out of play at the back post.
The Hoops' first real chance came on the quarter-hour when former Don Mulgrew's corner was headed over by Victor Wanyama.
Two minutes later the strong running of Watt saw him get by Mark Reynolds on the right before crossing for Georgios Samaras, but the Greek striker's clever dink deflected away for a corner off Russell Anderson.
Both sides were now beginning to probe and when Rae won the ball in midfield he fed the precocious Fraser, who tested Forster with a right-footed effort from 20 yards.
Celtic came closest yet as Commons retrieved a half-cleared Mulgrew corner on the left and swung a dangerous cross to the far post, where Watt headed off the base of the post.
Just after the half-hour, Chris Clark created space to cross from the left for the Dons and though McGinn got in the way of an initial header from Magennis, the former Celtic man reacted quickly to send a low shot narrowly wide of Forster's right-hand upright.
The Dons made a change at the interval with Robertson replacing Rae, who had been touch and go before the match. And the home side had some pressure early in the second half, culminating in a Magennis throw being headed narrowly over by Anderson.
Celtic were presented with a fine opportunity when Andrew Considine brought down Commons 22 yards out. Mulgrew took the free-kick but looped his effort high and wide of the far post.
Aberdeen were dealt a blow when Fraser was again forced off just after the hour, limping from the pitch to be replaced by Scott Vernon.
The Dons were undeterred, however, and after 68 minutes they had their best chance yet. McGinn cut the ball back for Hayes, and the Irishman set himself before firing low into the side netting.
But the deadlock was finally broken five minutes later, and the goal came for Celtic. Wanyama crashed a 25-yard shot off Jamie Langfield's left-hand post, and all newcomer Nouioui had to do was roll the ball home.
Boosted by their goal, Celtic added a second just three minutes later. Samaras crossed from the left and, at the back post, Mulgrew acrobatically volleyed home left-footed.
The visitors had the ball in the net again when Wanyama headed home at the back post, but the flag had already been raised for offside against the Celtic man.