Early Aberdeen pressure saw a deep cross from Alan Maybury find the head of Derek Young whose powerful effort from eight yards flew just over the crossbar.
An outswinging corner from Shunsuke Nakamura after five minutes was headed just over at the near post by skipper Stephen McManus.
Around the ten-minute mark both sides traded good chances within 60 seconds of one another.
Celtic's Aiden McGeady floated in a cross which found the head of Scott Brown and the midfielder's effort crashed of the face of the post with full-back Jackie McNamara on hand to clear the danger.
Aberdeen drove to the other end of the park where a Barry Nicholson cross saw Young get the better of Andreas Hinkel before playing the ball back into the path of Darren Mackie, who carelessly stabbed his shot wide of the upright with the goal at his mercy.
The champions took the lead on 16 minutes, McGeady skipped away from Maybury before driving the ball low across the area to find Nakamura, who had the easiest of tasks to sweep the ball into the unguarded net.
A cleverly worked free-kick by Aberdeen almost had them back on terms on 23 minutes. Josh Walker picked out Dave Bus' late run into the area where the centre-back nodded the ball back across the goal, but the onrushing Richard Foster couldn't keep his fierce effort on target.
The home side were taking the game to Celtic at every opportunity and could have scored again on 29 minutes. Brilliant link play between Lee Miller and Mackie saw Miller feed the ball into his strike partner's path and his left-foot shot from inside the area beat Artur Boruc, but cannoned away off the post.
Celtic increased their advantage in 34 minutes, McGeady picked up a loose ball in midfield before waltzing past McNamara and firing home an unstoppable left-foot effort which crept just inside the upright.
Celtic were unrelenting and increased their advantage just before the interval. Walker had gone in recklessly on Scott McDonald to leave referee Craig Thomson with the easy decision to award a penalty kick. The Aussie dusted himself down before comfortably netting.
Aberdeen did have an opportunity to get one back, but Foster wasted a great position as he lifted a gilt-edged chance over the bar.
Sublime skill by McGeady then bamboozled the Dons defence, before he clipped the ball up to the far post to leave the unmarked McDonald an easy header to make it 4-0.
It was almost a total rout on the hour, with Jamie Langfield excelling, firstly to stop a great shot from Nakamura, then with McDonald wriggling free of his marker, the Dons keeper somehow tipped his goalbound effort over the bar.
After 62 minutes slack play inside the Celtic box saw efforts from Mackie and Young not being properly cleared. The ball finally broke into the path of Lee Miller, who drove the ball high into the net to pull a goal back.
Celtic finally got the fifth goal their scintillating play deserved when Barry Robson made a dream debut, scoring direct from a 20-yard free-kick in the 74th minute.