Luongo left the game late in the opening period after his skate was clipped by the Jets' Dustin Byfuglien with the Canucks holding a 1-0 lead. The team did not immediately disclose the nature Luongo's injury.
Lack surrendered an equalizer by Winnipeg's Evander Kane midway through the second but shut the door from there.
Chris Tanev's goal off a pass from Zack Kassian halfway through the final period put Vancouver ahead to stay and the Canucks went on to claim a ninth win in 11 games.
Brad Richardson scored on a first-period power play.
Ondrej Pavelec made 23 saves for Winnipeg.