Following a fairly uneventful opening half, the Hoops took the lead in the 51st minute from the penalty spot after Kenny Haswell had brought down Theodore Bjarnason, Jim O'Brien making no mistake with the resultant kick.
With eleven minutes remaining, Celtic made certain of the points when a through ball from Aberdeen target Rocco Quinn found Nicky Riley who beat Derek Soutar with a low shot.
Two Aberdeen players, skipper Jamie Winter and defender Neil McVitie, received yellow cards in the second half.