The Canadiens evened the Eastern Conference quarterfinal series at 1-1, but now must travel to Ottawa for Games 3 and 4 on Sunday and Tuesday.
All of the scoring came in the second period and it was started by the sudden outburst from White and Gallagher. White scored on a backhander 3:20 into the middle stanza.
Ottawa cut its deficit in half on a goal from Milan Michlak, but Michael Ryder restored the two-goal advantage with 1:03 remaining in the period.
Montreal earned the victory despite the absence of captain Brian Gionta, Max Pacioretty and Lars Eller -- all out with injuries.
Eller stayed in a hospital Thursday night after suffering a violent hit to the head by Ottawa defenseman Eric Gryba during the series opener on Thursday. Gryba was handed a two-game suspension by the NHL for the hit.