July 5 (Reuters) - Montreal netminder Carey Price kept alive his team"s slim hopes of winning the Stanley Cup as the Canadiens emerged with a 3-2 overtime victory over the defending champion Tampa Bay Lightning in Game Four on Monday. Price made 32 saves, including several key stops in overtime, before Josh Anderson"s second goal of the game sealed victory for the Canadiens, who now trail Tampa Bay 3-1 in the NHL"s best-of-seven championship series. Alexander Romanov had Montreal"s other goal while Price, who was shaky in a 6-3 loss that pushed his team to the brink on Friday, flashed the brilliant form that helped his team reach the final. "We are a resilient group," said Price, whose team were a 50-to-1 longshot when the playoffs began and overcame a 3-1 series deficit in the first round. "We faced adversity all season long and have responded well and we got a lot of work left to do," he told reporters. Barclay Goodrow and Pat Maroon scored for Tampa Bay, who twice came back from one-goal deficits but failed to take advantage of a golden opportunity with a four-minute powerplay that spanned the third period and start of overtime. "We had chances to end that sucker in regulation. Sometimes you can play well and like your game and you don"t win," said Tampa Bay head coach Jon Cooper. "You can"t pick your adversity, you have to fight your way through it. "It is why you go up in series, to give yourself a chance or multiple chances to knock a team out and now we have to regroup and see if we can do it in Game Five." DAUNTING TASK Montreal are in search of a record-extending 25th Stanley Cup but it would be Canada"s first since they last won it in 1993. Of the 27 previous teams to fall behind 3-0 in the Stanley Cup Final series, only the 1942 Toronto Maple Leafs fought back to win. Despite the daunting task facing Montreal, Canadian Prime Minister Justin Trudeau is not giving up hope. "It"s not over "til it"s over," he tweeted after the game. Montreal grabbed their first lead of the series with under five minutes left in the opening period when Nick Suzuki found Anderson alone in front of the net and the forward sent his shot over the glove of Andrei Vasilevskiy. Tampa Bay tied the score late in the second when Ryan McDonagh corralled a rebound outside the crease and flipped a no-look pass to Goodrow, who fired it into a wide-open net with Price out of position. Montreal moved in front midway through the third period when Romanov scored his first career playoff goal but Maroon tied it up five minutes later. Montreal lost captain Shea Weber to a four-minute high-sticking penalty with a minute left in regulation and while the Lightning had chances to put the game away the Canadiens stood firm before Anderson slammed home a loose puck for the win. Tampa Bay, who won last year"s Stanley Cup without any fans present inside the NHL"s biosecure bubble in Edmonton, will host Montreal when the series resumes on Wednesday with their arena at full capacity. "Obviously we are in a tough situation but we are still alive so we"re looking forward to the opportunity to go to Tampa and steal one there," said Anderson. Reporting by Frank Pingue in Toronto; Additional reporting by Steve Keating; Editing by Peter Rutherford