The opening goal from Maciej Zurawski was the highlight of the match as the Pole started to justify his transfer value with three goals in his last two matches.
Stilian Petrov added a second on the hour mark to ensure there was no way back for Aberdeen, who must have been disappointed with their performance, especially that of their strikeforce of Steve Lovell and Steve Crawford who were in Bobo Balde's pocket all afternoon.
Before kick-off there was a minute's applause for the late Jock Stein on the 20th anniversary of his death and an emotional welcome for some of his 1967 European cup-winning team.
Celtic threatened early when John Hartson just failed to get a touch to Alan Thompson's free-kick after Richie Byrne had fouled Shunsuke Nakamura.
Celtic took the lead thanks to a tremendous finish from Zurawski. The striker collected Balde's long clearance and played a neat one-two with Hartson. He was still 30 yards from goal but showed great composure before finishing with a fine shot high into the top corner.
Celtic player Mo Camara surged down the flank and won a free-kick at the edge of the box. Thompson's cross was headed out by Kevin McNaughton as Hartson threatened.
Aberdeen were playing some neat possession football without ever really threatening the Celtic defence. From a McNaughton cross Lovell did glance a header wide, before the Aberdeen striker was then denied by a strong challenge from Balde as he threatened to break clear.
Petrov wasted a good opportunity for the home side when he crossed weakly against McNaughton. Celtic then threatened with a swift counter attack after Nakamura intercepted a Scott Severin pass.
The ball was quickly transferred to Zurawski who laid it wide to the supporting Paul Telfer whose cross was deflected for a corner.
Ryan Esson looked commanding in the Aberdeen goal and held Camara's deep cross well under pressure from Hartson.
Artur Boruc in the Celtic goal showed that he also possessed some skills when he neatly side-stepped the on-rushing Lovell before clearing.
Telfer laid the ball off to Neil Lennon but the Celtic skipper shot wide.
Esson just beat Hartson to a fiercely driven Thompson cross and Aberdeen must have been relieved only to be one down at half-time.
Lovell's flick at the start of the second half for once found Crawford but Balde stepped in to concede a corner.
In a flowing Celtic move Hartson laid the ball off to Camara who wasted the chance by over-hitting his cross, much to the frustration of Hartson.
From Thompson's cross Hartson found Petrov but the Bulgarian did not connect properly with his shot and Esson saved diving to his right.
Aberdeen then nearly equalised but it was no surprise that it was Celtic defender Balde who placed his own keeper under pressure with a misdirected header from Barry Nicholson's cross.
Thompson should have done better than head over Nakamura's cross from close range but that miss was forgotten when Celtic went two ahead shortly afterwards.
Alexander Diamond ushered Zurawski away from goal but allowed the Pole room to turn and get in a cross which reached Petrov at the back post, who angled his shot into the corner of the net.
Aberdeen tried to respond but substitute Scott Muirhead volleyed Nicholson's cross high over.
Camera was again guilty of giving away possession with Hartson pleading for a cross to the back post.
Celtic manager Gordon Strachan sent on Craig Beattie and Shaun Maloney for the last 20 minutes with Esson doing well to hold Maloney's deflected shot.
Both substitutes posed problems for Aberdeen and after Beattie skipped past Russell Anderson he went down in the penalty area under a challenge from former Celt Jamie Smith, but his appeal was dismissed.
Beattie then created another chance for Zurawski but the striker was eventually crowded out as Celtic ran out comfortable winners.
Man of the Match: Maciej Zurawski – The Poland striker has suddenly found his form and scored another cracker to send the Bhoys on their way to a win.