Calgary overcame a 4-0 deficit to force overtime, with Chris Clark tying it with 7:04 left in regulation play.
But Morrison sent the series back to Vancouver for Game 7 on Monday, beating goalie Miikka Kiprusoff to end the longest game of the season and the longest in Vancouver history.
Geoff Sanderson, Jarkko Ruutu, Daniel Sedin and Brad May also scored for the Canucks. Martin Gelinas, Ville Nieminen and Oleg Saprykin added goals for the Flames.
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