The Capitals took a 3-1 lead in the Eastern Conference quarterfinal series and can advance to the next round when they host Game 5 Friday.
Washington avoided falling behind by two games to start the series when they survived an overtime encounter in the second contest. The Capitals then swept two games from the Canadiens in Montreal by a combined score of 11-4.
Montreal grabbed a 2-1 advantage on a power-play goal by Brian Gionta with 4:18 to play in the second period but Semyon Varlamov then held the Canadiens in check until the final moments while Washington was taking control.
The Capitals scored a vital shorthanded goal when Mike Knuble tied it with 7 seconds left in the second period.
Ovechkin put Washington in front for good with his second goal of the game and his fourth of the playoffs. He beat Carey Price with a slapshot with 8:51 left in regulation and Chimera scored 58 seconds later.
In the game's final 2:30, both Knuble and Nicklas Backstrom scored empty-net goals for the Capitals and Dominic Moore put in a backhander for the Canadiens.
Varlamov, who took over goaltending duties early in Game 2 after Jose Theodore allowed goals on each of the first two shots he saw, made 36 saves. Price allowed four goals on 35 shots.