Luongo had his leg clipped by big Winnipeg defenseman Dustin Byfuglien, and was knocked flat during a goal-mouth collision with Blake Wheeler. The goalie left a few minutes later, with 3:30 left in the first period.
Canucks coach John Tortorella said only that Luongo had a lower-body injury and is day-to-day. Vancouver's next game is Dec. 29 at Calgary.
Tortorella said Luongo had spoken with trainer Mike Burnstein briefly a couple of shifts earlier, but the coach had no idea the goalie was in any trouble.
"I didn't know," Tortorella said. "It surprised me."
The Olympic gold medallist was replaced by Eddie Lack. Luongo is one of the goalies being considered to play for Canada in the Sochi Olympics.
Lack made 15 saves to improve to 6-2-0.
"I was a bit surprised, for sure," Lack said. "I didn't hear anything before that he was hurt. I just stuck my glove on and got out there."
"I'm just trying to get pucks to the net," Tanev said. "It seemed like the seas parted when I got it. It was awesome when I walked into it."
Brad Richardson opened the scoring for Vancouver on a power play midway through the first period.
"You can't depend on just a couple of guys," Tortorella said. "I don't think this team for the last little while has. I think everybody has kind of chipped in."
Evander Kane tied it on a power play in the second.
"We had some opportunities to score, but I thought we didn't push the pace that we needed to," Kane said. "Not having the success now, it's very frustrating. It's not something you want to be part of. We're going to have to figure out a way to change that and get out of that rut."
Vancouver improved to 22-11-6 and is tied with San Jose for fifth place in the Western Conference. The Canucks have won nine of their last 11 games.
Winnipeg has lost five of its last seven games and is 11th in the West at 16-17-5.
"I thought we carried a fair bit of the play, but there's a difference between carrying the play and finishing your plays," Winnipeg coach Claude Noel said. "It isn't about scoring chances. We just couldn't close out the game. That was the disappointing part."
David Booth's assist on Tanev's goal was his 100th career assist. ... Vancouver defenseman Kevin Bieksa played his 500th NHL game. ... Vancouver's Tom Sestito and Winnipeg's Anthony Peluso fought in the first period.