The Canadiens lead the best-of-7 series 3-2. Game 6 is in Montreal on Friday (7 p.m. ET; CBC, TVAS, SN, ESPN2, The Spot).
Brendan Gallagher and Kirby Dach also scored for the Canadiens, who are the No. 3 seed in the Atlantic Division. Jakub Dobes made 38 saves, including 17 in the third.
Dominic James and Jake Guentzel scored for the Lightning, who are the No. 2 seed in the Atlantic. Andrei Vasilevskiy made 21 saves.
Texier made it 3-2 at 1:06. He took a stretch pass from Lane Hutson, skated into the left face-off circle and scored with a wrist shot to the far side that deflected off of Vasilevskiy's glove and into the net.
Gallagher, who was a healthy scratch in the first four games of the series, gave Montreal a 1-0 lead at 3:00 of the first period. Alex Newhook got his own rebound off the end boards and had the puck knocked away at the edge of the crease before Gallagher buried it from in front.
James tied it 1-1 at 6:49 of the second period. After Gage Goncalves dug the puck out in the defensive zone, he fed James to start a 2-on-1. James looked off a pass to Ryan McDonagh and put a snap shot under the glove from the right circle.
Dach put the Canadiens ahead 2-1 just 11 seconds later. He made a strong move to the net, lost the puck while fighting off a poke check from Vasilevskiy and scored past the glove at 7:00.
Guentzel tied it 2-2 at 17:23. He faked a pass to Oliver Bjorkstrand on a 2-on-1 and whipped a shot from the right circle through Dobes’ five-hole.