The Bruins fired 48 shots at New York goaltender Henrik Lundqvist to open the Eastern Conference semifinal series, finally getting the winning goal in what was Boston's second straight overtime victory.
Boston reached the semifinals with a 5-4 win over Toronto in Game 7 of their first-round series, the Bruins rallying from a three-goal deficit in the third period to pull off the unlikely comeback.
The Bruins outshot New York 16-5 in Thursday's overtime. The winning goal came when Patrice Bergeron, hero of Boston's Game 7 win over Toronto, went on a rush down the right side and fired a shot from the circle.
Marchand got his stick on it to tip it past Lundqvist.
Zdeno Chara scored midway through the first period to give the Bruins the lead, but the Knicks tied it with 2 seconds left in the period on a goal from Ryan McDonagh.
New York took its only advantage of the contest a mere 14 seconds into the third when Derek Stepan beat Tuukka Rask. Torey Krug tallied for the Bruins less than 3 minutes later.
Rask stopped 33 shots to get the victory. Boston will host the second game of the series on Sunday.