In the fifth round, Kassian faked to the backhand and slipped the disc past Miikka Kiprusoff. Curtis Glencross had the last chance for Calgary, but his wrist shot was stopped by Cory Schneider.
Kassian also scored in regulation as did Mason Raymond for the Canucks, who avoided their first 0-3-0 start since the 2009-10 season. Schneider made 34 saves in the win.
"He was great," Canucks forward Henrik Sedin said about Kassian. "He's a big body, he holds on to the puck and when he has confidence he can make a lot of plays for himself."
Alex Tanguay and Mikael Backlund each scored a goal for the Flames, who are 0-2-1 for the first time since 2007-08 season. Kiprusoff stopped 34 shots in defeat.
After a scoreless first period, Vancouver took a 1-0 lead at the 6:20 mark of the middle stanza. After a left circle faceoff win, Vancouver controlled the puck and Kassian tried a wraparound from the right side. Kiprusoff stopped the puck, but it came back to Kassian and his first shot from the right circle was stopped, but again the rebound came to him and he buried his third chance for a 1-0 lead.
Exactly two minutes later, the Canucks made it a 2-0 game. Daniel Sedin fired a pass from the top of the right circle over to the left for Raymond, who slid over to the slot and snapped a shot into the left corner for his first of the season.
Calgary, though, answered with a goal at the 11-minute mark to make it a one- goal game. On a 2-on-1 rush, Tanguay ripped a shot from the right circle that went off the left post and in to make it a 2-1 game.
The Flames then went on an extended power play as Vancouver took three minors over a span of 2:17. While skating 5-on-4, a rush from the Flames saw Jarome Iginla bring the puck in down the right wing and send a short pass over to Backlund, who snapped a shot off the right post to tie the game with 3:57 to play in the middle frame.
Schneider stopped 18 shots over the third period and overtime while Kiprusoff had to make just eight saves over that span to send it to a shootout.
Vancouver plays at Anaheim on Friday ... Calgary hosts Edmonton on Saturday ... Each team won three games in the series last season ... Vancouver was 1- for-4 on the power play while Calgary went 1-for-5.
01/24 03:25:08 ET