Vancouver's Cory Schneider and Calgary's Miikka Kiprusoff each gave up a goal over the first four rounds, but Kassian then came through for the Canucks and Curtis Glenncross could not answer for the Flames.
It was Vancouver's first win of the season after opening the campaign with two setbacks -- one of them in overtime. Calgary has yet to win in three tries.
All of the scoring during the regulation 60 minutes came in the second period. Kassian and Mason Raymond tallied during the first 8:20 of the period, after which Alex Tanguay and Mikael Backlund scored for the Flames.
Both goaltenders stopped 34 shots during regulation.
Costly malfunction causes beer flood at Boston-area brewery
Megyn Kelly: Santa Claus and Jesus are both white men