Rask made 15 saves in the second period as Boston was scoring three times to take control of the game.
David Krejci supplied a goal and two assists and Milan Lucic distributed three helpers for Boston, which grabbed the advantage in their best-of-seven Eastern Conference quarterfinal series with a convincing road win.
Phil Kessel and Jake Gardiner scored for the Maple Leafs, who were flattened in their first post-season home game since 2004.
James Reimer made 33 saves in the loss.
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