Anderson snapped a six-game goal drought on the sequence.
Suzuki, meanwhile, extended his point streak to three consecutive games.
That s the way things stood after 20 minutes. Tampa Bay held a 12-5 advantage in shots at the break.
Winger Barclay Goodrow tied things up 1-1 for the Lightning with 2:40 left in the second period, beating a helpless Carey Price for his second goal of the playoffs.
Goodrow was the beneficiary of a perfect feed from defenseman Ryan McDonagh, which led to the easy tally.
Center Blake Coleman also assisted on the goal.
That s the way things stood after 40 minutes. Tampa Bay was still outshooting Montreal by a 20-14 margin.
The Lightning came out looking determined to end things at the start of the game, getting the first eight shots on goal and outshooting the Canadiens 12-5 in the first period. It was the Habs, however, who took a 1-0 lead into the intermission thanks to Anderson as well as Carey Price.
Barclay Goodrow responded for Tampa Bay late in the second period to tie the game. Alexander Romanov put Montreal back on top in the third, only for Patrick Maroon to even things up again.
Shea Weber took a double-minor penalty for a high stick on Ondrej Palat that drew blood with just over a minute to go in the third, giving the Bolts a four-minute power play that carried over into overtime.
Montreal Canadiens avoid Stanley Cup Final sweep with OT victory against Tampa Bay Lightning
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Canadiens prevail in OT to force Game 5 (3:30)
The Canadiens send the series back to Tampa and avoid the sweep thanks to a pair of goals from Josh Anderson, including the overtime winner in Game 4. (3:30)
Daunting for most teams. Perfectly on brand for the Canadiens. Nothing has been easy for us all year. It wasn t going to start this series, veteran forward Brendan Gallagher said. We ve kind of accepted the fact that it s never going to be easy here.
Josh Anderson scored the game-winner less than four minutes into overtime his second goal of the night as the Canadiens avoided becoming the first team in 23 years to get swept in a Stanley Cup Final in a 3-2 win over the Lightning at the Bell Centre in Montreal. The victory extended the series to Wednesday s Game 5 in Tampa, Florida. The Lightning, meanwhile, fell to 0-4 in overtime this postseason.
Mark Blinch/Getty Images MONTREAL Josh Anderson delivered in overtime, and Montreal killed Tampa Bay’s chance for a Stanley Cup sweep. Anderson said the Canadiens weren’t done, and he was right at least for one night. The speedy winger scored his second goal 3:57 into overtime, and the Canadiens avoided elimination by defeating the defending champion Lightning 3-2 in Game 4 on Monday. “We didn’t want to end it tonight in front of our fans. We expected to go to Tampa tomorrow,” Anderson said. “I think everybody in that locker room did, you know, packed our bags this afternoon.”
Montreal Canadiens Tampa Bay Lightning Stanley Cup Final Game 4 Josh Anderson tsn.ca - get the latest breaking news, showbiz & celebrity photos, sport news & rumours, viral videos and top stories from tsn.ca Daily Mail and Mail on Sunday newspapers.