Montreal advances to play the Buffalo Sabres in the Eastern Conference Second Round. Game 1 is in Buffalo on Wednesday (7 p.m. ET: TNT, truTV, HBO Max, SN, CBC, TVAS).
All seven games in the series were decided by one goal and four went to overtime.
Montreal advanced despite being held to nine shots on goal in Game 7.
The game-winning goal came when Lane Hutson took a shot from the point that Andrei Vasilevskiy turned away with a stick and the puck went off the end boards where Newhook swiped at the airborne puck from the goal line and it went off of Vasilevskiy's back and into the net.
Nick Suzuki also scored for the Canadiens, who were the No. 3 seed in the Atlantic Division. Jakub Dobes made28 saves.
Dominic James scored for the Lightning, who were the No. 2 seed in the Atlantic. Andrei Vasilevskiy made seven saves. The Lightning were eliminated in the first round for the fourth consecutive season.
Suzuki gave the Canadiens a 1-0 lead at 18:39 of the first period after he tried to redirect a shot from Kaiden Guhle at the hashmarks and the puck went off J.J. Moser's shin and into the net.
James tied it with a power-play goal at 13:27 with a redirection from the slot off a slap shot by Charle Edouard D'Astous from the point.
