Victor Hedman and Ross Colton scored for the Lightning (38-15-6), who ended a three-game losing streak.
Tampa Bay lost 4-1 to the Edmonton Oilers on Saturday and could not travel until Sunday afternoon because of a mechanical issue with the team plane.
"Talking to the guys, we didn't want to have any of this travel and all the issues we had last night and the late night and say 'Well, we're going to mail this game in,'" Lightning coach Jon Cooper said. "No excuses from this group, and they came through."
J.T. Miller scored, and Thatcher Demko made 29 saves for the Canucks (29-24-7), who lost in regulation for the first time in five games (3-1-1). They played without center Elias Pettersson; he is day to day because of an upper-body injury.
"We tried, we played really hard in the last two periods," Vancouver coach Bruce Boudreau said. "Sometimes you're playing a world-class goalie, arguably the best goalie in the world. We had some really great chances, [but] we couldn't get it by him. We got one, but he was the one who was the difference maker for their team."