Bozak's power-play goal during a scrum around the Ottawa net 5:42 into the final frame put the Leafs ahead for good and Toronto went to keep its flickering playoff hopes alive with a sixth win in seven games.
Tenth-seeded Toronto pulled to within three points of the New York Rangers for the eighth and final seed with three games to play.
Phil Kessel, Nazem Kadri and Nikolai Kulemin also found the net and James Reimer stopped 23-of-25 shots for the Leafs.
Jason Spezza scored both goals for Toronto and Craig Anderson made 26 saves for the Senators.
Notable deaths of 2014 [PHOTOS]