Lupul's tallies erased a 1-0 deficit and put the Maple Leafs on the path to their first post-season victory since 2004.
Phil Kessel's breakaway goal on a pass from Nazem Kadri 53 seconds into the final frame put Toronto ahead by two.
Johnny Boychuk scored for Boston midway through the third, narrowing the Leafs' lead, but James van Riemsdyk added an insurance goal with 3:07 remaining and Toronto went on to forge a 1-1 tie in their Eastern Conference quarterfinal series.
James Reimer turned aside 39-of-41 to earn the victory.
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