The Bruins went ahead to stay, 3-2, at 12:08 of the second period when Boychuk, who had one goal in the regular season, shot a 40-footer inside the near post for his third playoff goal.
The Swans defence held off striker Keogh's rampaging run but the Irish international fed Peter Whittingham whose 25-yard left-footer just whistled past de Vries' left-hand post.