With the Bruins' Dennis Seidenberg off the ice for cross-checking, Kessel scored on the power-play midway through the third to make it 3-3. It was the first goal in 15 games for all-star winger.
Grabovski scored on a snap shot with 1:01 remaining to give the Maple Leafs their third win in five games.
James Reimer stopped 32-of-35 shots for Toronto.
Gregory Campbell had a goal and an assist and Patrice Bergeron and Daniel Paille each scored a goal for the Bruins, who entered the contest with a one-point lead over Montreal in the Northeast Division.
Tim Thomas turned aside 24-of-28 shots for Boston.