The victory gave the Senators the seventh seed for the Eastern Conference playoffs and a matchup with Montreal and dropped the New York Islanders into eighth and a first-round series against the Pittsburgh Penguins.
The Bruins, who could have won the Northeast Division and earned a No. 2 seed with a win, finish fourth; they will play Toronto in the first round.
The game was originally scheduled for April 15, the day of the Boston Marathon bombings. It was the only NHL game on Sunday, with the rest of the league wrapping up the regular season by Saturday.
Kyle Turris scored an empty-netter with 37 seconds left.