The Celtics rallied from a five-point deficit in the final 5 minutes of regulation and had a chance to take a three-point lead when Ray Allen went to the line with 17 seconds left. Allen, however, made just one try and Carlos Delfino's layup with 11 seconds to go forced overtime.
Pierce made eight free throws in the extra period, the last two giving the Celtics a three-point cushion. Daniels then took the ball away from Delfino to prevent a Milwaukee attempt at a 3-pointer.
Pierce scored 28 points and Allen had 23, bringing Boston its fourth win in five games to start the season.
Andrew Bogut had 21 points and 13 rebounds for the Bucks, who have won once in five tries.