Sam Montembeault once again got the start in goal. And with Kaiden Guhle sidelined with a lower-body injury, Chris Wideman returned to the lineup for the first time since Monday night versus Colorado.
The Canadiens opened the scoring just past the five-minute mark of the first, when Jesse Ylonen forced a turnover deep in the Tampa zone, allowing Nick Suzuki to feed the puck to a wide-open Mike Hoffman, who wristed it in from the hash marks for his 12th of the season.
Victor Hedman tied the game at 11:31 of the opening frame.
After 20 minutes, the teams were even at 1-1 with Tampa outshooting Montreal 13-6.
In the second, Brandon Hagel gave the Lightning their first lead of the night at 4:50 of the frame.
But Denis Gurianov squared things up a bit more than 90 seconds later when he one-timed Josh Anderson's pass from the corner in past Sergei Bobrovsky to make it a 2-2 game.
Anderson and Suzuki earned the assists.