The Bruins and Montreal are tied with 61 points, but Boston have two games remaining, while the Canadiens only have one.
Dennis Seidenberg and Daniel Paille scored in the second period, while goalie Tuuka Rask took care of the rest as the Bruins won, despite being outshot 30-24.
St Louis’ Ryan Reaves scored twice in the Blues’ 4-1 win over the Calgary Flames, while goalie Brian Elliott earned his NHL-leading 10th win this month.
New York captain Ryan Callahan scored the overtime winner as the Rangers rallied to beat the Carolina Hurricanes 4-3 and clinch an Eastern Conference playoff berth.
Detroit moved closer to a 22nd straight playoff appearance by beating the Nashville Predators 5-2, with Pavel Datsyuk having a goal and two assists for the Red Wings.
Toronto’s Phil Kessel scored twice to lead the playoff-bound Maple Leafs to a 4-0 win over the last-placed Florida Panthers.