Marchand scored off the rebound of Patrice Bergeron's shot.
Game 2 is Saturday in Ottawa.
Trailing 1-0 and without a shot since the first period, the Bruins had two quick ones and Vatrano beat Anderson from the high slot on the second to tie it at 4:55 of the third.
Boston was outshot 12-0 in the second and was fortunate to trail by just one.
Despite having played the least amount of any player in the first period with just 2:20 of ice time, Ryan was creating chances every time he was on the ice and nothing changed in the second.
The Bruins had a scare when Colin Miller left the game early in the second after being hit by Mark Borowiecki. With an already depleted blue line, the Bruins can hardly afford to lose another defenseman. Miller returned to the game later in the period.
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