Tampa Bay controlled possession for long stretches of the first period, but it was the Habs who emerged with the lead at the end of 20 minutes. Late in the period, space opened up for Nick Suzuki on the left wing and he drove down low before finding Josh Anderson open in the slot for a one-timer that got past Andrei Vasilevskiy.
The goal came on only Montreal's second shot on goal of the game and gave the Habs their first lead of the series.
It took until late in the second period for the Lightning to get on the board themselves. Ryan McDonagh stepped up at the blue line to hold the play in the offensive zone and then went to the front of the net. After Carey Price made a save on Blake Coleman's point shot, McDonagh gathered the rebound and sent a no-look pass to the slot for Barclay Goodrow to quickly snap home.
Montreal went back in front at the 8:48 mark of the third when Alexander Romanov's shot from the point beat Andrei Vasilevskiy with Artturi Lehkonen providing the screen in front.
It took less than five minutes for the Bolts to respond with their second equalizer of the game to force overtime. On an odd man rush, Pat Maroon kept his stick on the ice and drove to the far post to redirect Mathieu Joseph's feed past Price and tie the game at two.
Overtime followed an all too familiar script for the Bolts, with a late power play chance wasted and an opposing game-winner following shortly.
In Game 4, it was a four-minute power play chance gifted to the Bolts by Shea Weber because of a high-stick to Ondrej Palat. After falling to convert in the final minute of regulation, the Bolts also wasted the carry over three minutes in the extra session.
Shortly after getting back to full strength, Cole Caufield poked the puck free for Anderson at the far post and he quickly fired a shot past Vasilevskiy to get the Habs on the board in the series.
The two teams will now return to Tampa for Game 5 of the Stanley Cup Final on Wednesday night at Amalie Arena.
Scoring Summary
1st Period
MTL | 15:39 Josh Anderson (4) - Nick Suzuki, Cole Caufield
2nd Period
TBL | 17:20 Barclay Goodrow (2) - Ryan McDonagh, Blake Coleman
3rd Period
MTL | 8:48 Alexander Romanov (1) - Jake Evans
TBL | 13:47 Pat Maroon (2) - Mathieu Joseph, Tyler Johnson
Overtime
MTL | 3:57 Josh Anderson (5) - Cole Caufield