Vegas fell behind 2-0 for the second consecutive game but rallied to beat Chicago Tuesday night in Toronto and win the series four games to one.
"We stuck to our game plan," said Tuch. "I thought we were playing well. We just needed a couple of lucky bounces.
"We knew our goaltender was playing well and would come up with some big saves."
Max Pacioretty, Mark Stone and Alec Martinez also scored and former Blackhawk goaltender Robin Lehner made 23 saves for top-seeded Vegas.
Jonathan Toews, Alex DeBrincat and Patrick Kane scored for the eighth-seeded Chicago. Goaltender Corey Crawford made 35 saves.
Tuch drove to the net with Chicago defenceman Adam Boqvist trying to cut him off, but Tuch managed to force the puck past Crawford to give Vegas its first lead 4-3 early in the third.
"I just tried to get a shot on net, maybe go for a rebound. I don't know what it hit," said Tuch.
Last Friday, Hart allowed four goals on 26 shots before being pulled halfway through a 5-0 loss in game two.
But the former WHL Everett Silvertip has been solid since, earning his first career playoff shutout in a 1-0 win in game three on Sunday.
'Best in the league' -
"He has been an absolute wall for us back there, he's so calm," Flyers defenceman Philippe Myers said.
"The way he's playing right now he's the best in the league."
Hart's best save came early in the second period off a hard shot by Montreal's Shea Weber that Hart got a piece of before it rang off the post.
"I think we've been good, but I don't think we really tested (Hart) much the last two games," Canadiens forward Phillip Danault said. "We have to get better around the net."
Michael Raffl and Philippe Myers scored for the Flyers, who seized a commanding 3-1 lead in the best-of-seven series.
Philadelphia can advance with a win Wednesday in game five.
Carey Price made 20 saves for the Canadiens, who have outscored the Flyers 6-5 in the series but have just one win to show for it.
Raffl opened the scoring at 6:32 of the first period, firing the puck into the top left corner of the net behind Price.
Myers got a lucky bounce to score the second Flyers' goal at 17:04 of the second. His soft shot towards the goal deflected off a defenceman's stick and then hit Price before going into the net.
In Edmonton, John Klingberg scored a third period goal as the Dallas Stars defeated the Calgary Flames 2-1 in game five of their series.
Klingberg carried the puck to the top of the faceoff circle and blasted a shot inside the right post after taking a pass from teammate Mattias Janmark.
The Stars now have their first lead in the series at 3-2. They can eliminate Calgary with another victory on Thursday.
Alex Ovechkin scored twice as the Washington Capitals rallied from a two-goal deficit to stay alive in the playoffs with a 3-2 victory over the New York Islanders. The Islanders lead the series three games to one.