Jake Evans also scored, and Phillip Danault and Brendan Gallagher each had two assists to help Montreal rebound from an opening overtime loss in Toronto.
''That's going to be a strength for us all year long,'' Gallagher said. ''We're pretty confident with the depth that we have. If we can hold each other accountable to show up and come at teams in waves like that . we can come at teams four lines deep. We feel like anyone who's on the ice can get the job done.''
Slater Koekkoek scored for Edmonton, spoiling Price's shutout bid with 7:01 left. Mikko Koskinen stopped 30 shots for the Oilers.
''They were definitely quicker than us,'' Edmonton star Connor McDavid said. ''We've got to be better, we've got to win more battles. They were definitely the more rested team and they showed that, but I didn't think our battle level was good enough.''
The teams will meet again Monday in Edmonton.
''Teams adjust. There's also a sense of revenge with a loss,'' Montreal coach Claude Julien said. ''We park this win and we take the two points because they're important, but then we have to realize we'll probably have an even tougher opponent two days from now.''
Petry scored on a power play 6:50 into the game after Caleb Jones was called for interference.
Tatar made it 2-0 early in the second, ripping a shot slap shot from below the face off dot over Koskinen's glove. Petry added another midway through the second period with a long shot from below the blue line that hit Oilers defenseman Ethan Bear and bounced into the net.
Gallagher sprang Tatar on a breakaway halfway though the third period, with the winger slipping a shot through Koskinen's legs.
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