Toronto took a 4-1 lead in the third period, but Boston cut the deficit to two midway through the period
and scored twice in the final 82 seconds to force overtime.
Tuukka Rask stopped 24 shots for Boston, which led the best-of-seven series 3-1 before the Maple Leafs won two in a row to force a seventh game.
James Reimer made 30 saves for the Maple Leafs. Cody Franson scored twice, and former Bruin Phil Kessel had a goal and an assist for Toronto.
No. 4 Boston will face sixth-seeded New York in the second round.
RANGERS 5, CAPITALS 0
Led by Henrik Lundqvist’s 35 saves in a second consecutive shutout, and goals from some unlikely sources, New York topped Washington in Game 7 on the road to reach the Eastern Conference semifinals.
New York contained Alex Ovechkin again and completed its comeback after trailing in the series 2-0 and 3-2 – the latest in Washington’s long history of playoff collapses.
It is the first time New York won a Game 7 on the road in its history.
Arron Asham put New York ahead in the first period, before Taylor Pyatt and Michael Del Zotto made it 3-0 early in the second on goals 2:10 apart.
Ryan Callahan added a goal 13 seconds into the third period, and when Mats Zuccarello scored with about 13½ minutes remaining, thousands of red-clad fans streamed to the exits.