Bergeron gave the Bruins a 2-1 lead at 1:51, but Brown tied it 2-2 at 3:04.
With the Bruins already killing a minor penalty for too many men on the ice, Marchand was called for a hooking minor and a double minor for spearing at 6:08. The Bruins killed 55 seconds of a 5-on-3 and then 1:05 more of an Ottawa 5-on-4.
"For sure, it definitely helped us," Bergeron said. "And they got some good looks, Tuukka made some great saves, but at the same time, I thought we did a good job overall and yeah, you often say that power play or penalty kill, special teams can give you some momentum, and I thought tonight it was the penalty kill that did it."
Danton Heinen put the Bruins ahead 3-2 at 5:43 of the third period, and Marchand made it 4-2 with a power-play goal at 6:50.
Jake DeBrusk made it 5-2 with 3:44 left.