Rask gave up a goal just 1:54 into the game, then blanked the Maple Leafs while the Bruins were cranking up their offense. A power-play goal from Nathan Horton with 12 seconds left in the first period put Boston in front for good.
The Bruins and Maple Leafs, two of the original NHL teams, met in the playoffs for the first time in 39 years and Toronto appeared in the postseason for the first time since 2004.
The Bruins tied it with 3:40 left in the first period on a slap shot from Wade Redden and Horton produced the go-ahead goal by tipping in a shot from Redden while Dion Phaneuf was serving a penalty for slashing.
Boston broke it open on second-period goals by David Krejci and Johnny Boychuk.
After winning the Stanley Cup two years ago, Boston was eliminated in the opening round of the playoffs by seventh-seeded Washington last season.
James Reimer, who posted a 19-8-5 record with a 2.46 goals-against average during the regular season, suffered the loss in his playoff debut. He gave up all four goals on 41 shots.