Crosby scored with 54.2 seconds left in regulation to force overtime and then scored the only goal in two tries for the Penguins during the shootout.
The win was the 232nd career victory for Pittsburgh coach Dan Blysma and moved him past Eddie Johnson to the top spot in team history.
Letang's goal at 18:49 of the third period cut Vancouver's lead to 4-3 and set the stage for Crosby's dramatic tying goal 16 seconds later.
Zack Kassian and Chris Higgins both scored a goal and assist for the Canucks. Eddie Lack made 31 saves.
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