Aberdeen did well to keep the game goal-less by half time with keeper James Langfield repelling a Celtic onslaught with a string of fine saves.
A stunning strike by Stilian Petrov broke the deadlock before Shaun Maloney scored the second from close range. The selfless Petrov laid on Maciej Zurawski's goal and Celtic's third on a plate.
The home team opened brightly and John Hartson's flick released Petrov, whose strike was deflected for a corner. The Dons keeper then had to look sharp to beat Petrov to a long through ball at the edge of his box.
The Dons' keeper did well to palm out a Roy Keane cross as Celtic dominated the early proceedings. From another Keane cross the ball broke off Alexander Diamond to Petrov, but from only eight yards the Bulgarian blasted his shot at the keeper.
The visitors threatened briefly with a long-range shot from Scott Severin which Artur Boruc gathered easily. Mark Wilson slipped at the edge of his own area, but Aberdeen couldn't take advantage with Steve Lovell eventually caught offside.
Barry Nicholson was carried off for the visitors after a wild Keane challenge which looked to have caught himo in the ribs, and the Celtic player was lucky not to be booked. Ferne Snoyl was next to limp off for the visitors after a strong challenge by Dianbobo Balde, and Aberdeen now had two of their substitutes, Richard Foster and Darren Mackie, on before half-time.
Keane nearly made the breakthrough just before the interval, but his 20-yard shot just cleared the bar. Balde did well to clear a Severin cross for a corner, but from Danny Griffin's cross Russell Anderson's header floated wide.
Foster neatly beat Balde on the half-way line and his pace carried him into the box, but rather than shoot the substitute elected to pass to Severin and the chance was lost. Aberdeen were causing more threat than in the first half..
After Maloney was fouled on the edge of the Dons box, Celtic boss Gordon Strachan replaced the ineffective Hartson with Shunsuke Nakamura.
Just when Aberdeen began to sense a chance of a win, they fell behind to a wonder strike from Petrov. The midfielder waited forZurawski's cut -ack before striking a 10-yard thunderbolt that entered the top corner before Langfield could react.
Celtic doubled their lead when Telfer found Keane and, after Chris Clark failed to clear his cross, Maloney stepped in to score from close range.
The home team finished with a flourish. Petrov was found superbly by Keane and, after side stepping the keepe,r he unselfishly laid the ball off to Zurawski, who shot home from 10 yards.