Horvat had an assist on Alexandre Burrows' goal into an empty net with 46.4 seconds left for the Canucks (13-16-2), who ended a three-game losing streak.
"We've had so many bounces that haven't gone our way," Horvat said. "To get one like that, it was kind of a relief off everybody's shoulders that we are going to start getting bounces here."
Luca Sbisa and Brandon Sutter also scored and Ryan Miller made 25 saves for the Canucks, who bounced back from an 8-6 loss to the Carolina Hurricanes on Tuesday to end a 1-4-0 road trip.
"It was a statement game after our last performance in Carolina," Sbisa said.
Defenseman Victor Hedman also scored and Vasilevskiy made 20 saves for the Lightning (15-14-2), who have lost four of five and eight of 10. Tampa Bay was missing injured top-line forwards Ondrej Palat and Nikita Kucherov, who leads the team with 30 points.
"It was a pretty solid effort by a depleted group and I feel for the guys," said Lightning coach Jon Cooper, who lamented turnovers on the first two Vancouver goals and an offensive zone holding penalty by forward Alex Killorn that led to the third. "It's a self-inflicted loss is what it is. A couple bad turnovers end up in our net and then a marginal call at best, but a penalty 200 feet from our net and they just get an unreal break. It's tough to fault the guys and their effort."