Hutson won it with a slap shot from above the right face-off circle after taking a pass from Alexandre Texier out of the right corner.
Montreal leads the series 2-1. Game 4 will be played here Sunday (7 p.m. ET; CBC, TVAS, SNE, SNO, SNP, ESPN, The Spot).
All three games have been decided in overtime.
Texier and Kirby Dach each had a goal and an assist, Zachary Bolduc had two assists, and Jakub Dobes made 15 saves for the Canadiens, the No. 3 seed in the Atlantic Division.
Brayden Point and Brandon Hagel scored for the Lightning, the No. 2 seed in the Atlantic. Andrei Vasilevskiy made 26 saves.
Texier and his newly formed line gave the Canadiens a 1-0 lead at 4:53 of the first period. Bolduc took Dach’s return pass along the right side and fed a backhand pass into the top of the slot for Texier, who snapped a shot past Vasilevskiy’s blocker from above the left hash marks.
Point tied it 1-1 with a power-play goal at 7:42. He scored on a snap shot past Dobes stick side from the right hash marks off Jake Guentzel’s pass from the right corner.
Hagel put the Lightning up 2-1 with an unassisted goal at 4:47 of the second period. He stuck out his left glove to cut off Jake Evans’ backhand pass in the neutral zone before driving in and going wide of Montreal defenseman Kaiden Guhle’s coverage to put a wrist shot past Dobes from the top of the left face-off circle.
Dach tied it 2-2 at 12:43. He turned back toward the net along the right boards to take a wrist shot that went off Tampa Bay defenseman Ryan McDonagh’s leg and got between Vasilevskiy’s pads.