A goal by Montreal's Tom Kostopoulos at 16:55 of the third period led to a 2-2 tie after regulation and the overtime was scoreless. In the shootout, Wheeler, the first shooter, lost control of the puck briefly then regained control and slipped it past Carey Price.
Milan Lucic and Matt Hunwick also scored, while Tim Thomas finished with 33 saves -- including the three stops on the shooters he faced in the shootout for the Bruins, who have won four in a row and nine of their last ten games overall.
Montreal's Andrei Kostitsyn scored in the second period. Price made 25 saves on 27 shots before Wheeler's game-winner for the Canadiens, losers in two of their last three outings.
There were no power play goals on six combined man-advantage opportunities.