Rask's whitewash was the 17th of his career.
Patrice Bergeron, Adam McQuaid, David Krejci, Chris Kelly and Shawn Thornton each scored for Boston, which notched a second straight victory on a three-game road trip and beat the Lightning for the second time this season.
Tampa Bay goalie Ben Bishop was victimized for four of the Bruins goals on 17 shots, losing for the first time in five starts to begin 2013-14.
He was pulled late in the second period. Anders Lindback finished up with four saves on five shots.
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