Marchand, who also had two in Boston's shootout loss in Chicago on Sunday, has scored six in his past four games. Torey Krug had the other goal for the Bruins, who won at home for the 11th time in 13 games.
Boston's backup goaltender Chad Johnson made 21 saves.
Los Angeles has lost two straight, but collected points in six of eight (4-2-2).
Marchand scored 18 seconds after Los Angeles had tied the game when he one-timed Patrice Bergeron's pass inside the right post by Quick's glove.