Kelly's goal late in the second period broke a 1-1 tie and the Bruins followed with two more in the final frame, improving to 13-0-1 in their last 14 games.
Rask turned aside 10-of-11 shots in the second period for Boston, which completed a home-and-home sweep of the Maple Leafs and improved to 4-0-0 against them this season.
David Kreji and Nathan Horton each contributed a goal and an assist in the victory.
Mikhail Grabovski got Toronto's only goal. James Reimer made 26 stops for the Leafs.