"As the game went on I got more confidence," Crosby said.
Crosby had a solid scoring chance just over a minute into the game, darting out from behind the net and flicking a backhander that Brodeur turned aside.
The Dallas Stars and New York Rangers both staged late rallies to win their season openers.
Jason Arnott scored a goal and set up three others, including Philippe Boucher's go-ahead tally with 4:46 left in the third period as the Stars rallied from a four-goal deficit to post a 5-4 triumph over the Los Angeles Kings.
Jaromir Jagr scored the tying goal 6.5 minutes into the third period and netted the game-winner five minutes later as the New York Rangers overcame a two-goal deficit and posted a 5-3 victory over host Philadelphia Flyers.
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