Tanev broke a 1-1 deadlock at 10:23 of the third with a shot from the high slot.
The Canucks (22-12-8) posted their ninth win in the past 11 games, while the Jets (16-17-5) lost for the fifth time in the past seven outings.
It was Vancouver's sixth consecutive home triumph.
Goaltender Eddie Lack picked up the win in relief of injured starter Luongo, who left the game late in the first period. Lack recorded 21 saves on 22 shots for his second consecutive win.
Winnipeg goaltender Ondrej Pavelec bore the loss while stopping 23 of 25 shots.
Luongo left the game with 3:30 remaining in the first period during a television timeout. He was replaced by Lack, who backstopped the Canucks to a 3-2 shootout win in Chicago on Friday.
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Rangers 4, Wild 1
The New York Rangers, trying to salvage the remainder of a nine-game homestand, knocked off the Minnesota Wild 4-1.
The win moved the Rangers (17-18-2) to just 2-4-2 on their longest ever home stand, which concludes on Monday against the Toronto Maple Leafs.
Minnesota (20-13-5) dropped their fourth game in their last six. The Rangers had not won a game in regulation since a 3-1 win at Buffalo on Dec. 5.
Coach Alain Vigneault's team overcame a 1-0 Minnesota first-period lead by scoring two goals in the second period and one in the third.
Cam Talbot, making his first start in goal for the Rangers since Dec. 2, stopped 24 shots to improve to 7-2. Niklas Backstrom (2-7-2) recorded 32 saves for the Wild.