After Boston let a two-goal lead get away in the third period, Seguin came through in the second round of the shootout while Tim Thomas was stopping Montreal's Rene Bourque, Max Pacioretty and Lars Eller.
A power-play goal by Patrice Bergeron, his 17th score of the season, put Boston in front 3-1 with 5:27 to go in the second period.
Pacioretty and Erik Cole then scored for Montreal in the third to force overtime.
Boston won for the third time in four games and finished the season series with Montreal by capturing four out of six.
Thomas made 26 saves.
Carey Price gave up three goals on 34 shots in addition to the wrister from Seguin that won the game. Montreal has lost in overtime 10 times this season, the fourth team to reach that plateau.
Ukrainian protestors topple Lenin statue [VIDEO]
Trader Joe's: Car crashes into Long Island store, injuring 11