Aberdeen arrived at Parkhead for the third time in the league this season in the knowledge that they had won on two of their last three visits there.
However a destructive second-half performance from Wales striker John Hartson handed Martin O'Neill's side an essential 2-0 victory that allowed them to reclaim pole position from arch-rivals Rangers.
The most recent encounters between these sides have enjoyed early goals but that was not to be repeated on this occasion.
Scott Severin's 13th minute effort was the game's first attempt on goal but Robert Douglas held the shot well. Stilian Petrov then fired wide after a quick Chris Sutton free-kick at the other end.
Celtic created an excellent opportunity in the 19th mintue. Didier Agathe broke free on the right and found Sutton on the byline. The Englishman cut the ball back for Hartson but Alexander Diamond blocked the frontman's shot, preventing a certain goal.
On half-hour mark Jackie McNamara made a vital contribution by clearing Russell Anderson's goalbound header off the line and Diamond's follow-up effort ended up way over the crossbar.
A minute later referee John Underhill waved away Alan Thompson's claim for a penalty - although television replays showed that Thompson had a fair point.
Darren Mackie fired the ball across the face of the Celtic goal in the final minute of the first half to worry the home supporters.
However, a minute after the restart Celtic went ahead. Thompson's deep free-kick from the right found Hartson at the far post, and although the Welshman didn't manage to get a clean shot on goal, the ball squirmed into the corner of Ryan Esson's net.
In the 58th minute Hartson headed another Thompson cross from the right narrowly wide but 13 minutes later the SPL's leading scorer was more accurate with his next attempt.
Sutton again made his way to the byline and pulled the ball back across goal where Hartson was perfectly placed to sidefoot a shot into the net.