Roy's first-period goal opened the scoring for St. Louis and his fourth-round goal against Tuukka Rask in the tiebreaker handed the Blues their 15th win in 21 games starting the season.
David Backes also scored for St. Louis.
Jaroslav Halak notched the victory with 29 saves.
Carl Soderberg and Gregory Campbell each scored for the Bruins.
Rask stopped 24 shots.
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