The Bruins moved within a point of idle Montreal for the best record in the Eastern Conference, getting 29 saves from Tuukka Rask.
Bergeron tipped in a shot with 5:04 to go in the first period to give the Bruins a 2-0 lead and his empty-netter came with 58 seconds remaining. He has eight goals for the season.
The only goal allowed by Rask was a shorthanded one produced by Shawn Matthias in the second period.
Scott Clemmensen surrendered three goals in 31 shots to take the loss.