Mason kept the Flyers in the game with 16 saves during a Rangers-dominated first period.
"He was huge," said winger Jake Voracek, whose power-play goal in the second period was the difference. "That was exactly what we needed - a game like that."
Game 5 is Sunday at noon at Madison Square Garden, where the Flyers ended a nine-game losing streak in that building in Game 2.
The Flyers are 14-7 in series that are tied at two wins apiece. They are 1-15 when trailing three games to one, showing the significance of Friday's outcome.
The Flyers' defensemen had to step up because the team was shorthanded after Nick Grossmann left the game with an apparent knee injury with 14 minutes, 35 seconds left in the second period. Grossmann did not return.
"They played awesome," said winger Wayne Simmonds, whose team admirably killed a critical four-on-three power play that lasted 1:27 and spilled into the early minutes of the final period. "We have a lot of unheralded defensemen on our team. They go out and do their job every night. They're responsible, and they allow us to win."
Braydon Coburn played 25:27 and had an assist, Kimmo Timonen played 23:36 and had three hits, Andrew MacDonald blocked five shots, Mark Streit assisted on the game-winner, and Luke Schenn had three hits.
Giroux vowed after Tuesday's 4-1 Game 3 loss that the Flyers would even the series Friday. Earlier in the season, after the Flyers started a franchise-worst 1-7, he predicted they would make the playoffs.
Voracek tipped in Brayden Schenn's drive while the Flyers were on a power play, giving the Flyers a 2-1 lead with 12:38 left in the second period.
"Schenn made a good heads-up play, and I just tried to go high," Voracek said.
It gave Mason his first lead in any of his six career playoff games, including four with Columbus in 2009. It also gave the Flyers their first home lead in the series, after 87:22.
Mason recorded his first-ever playoff victory.
The Rangers dominated the first 20 minutes and spent a majority of the period in the hosts' end.
But Mason stood tall, and the Flyers tied it on Matt Read's first goal of the series.
While on a three-on-three rush, Jason Akeson's shot deflected off Ranger defenseman Kevin Klein and off the backboards. Read swooped on the rebound and fired it past Henrik Lundqvist with 11:05 left in the first period.
"Akey made a great pass. He told me he meant to do that, throw the puck behind the boards, and it came right to me," Read said of Akeson. "I just had to one-time it. I think Lundqvist got a piece of it, but we'll take it."
The Rangers had taken a 1-0 lead when Dominic Moore rushed out of the penalty box and fired a shot that Mason turned aside, but the 33-year-old center gathered the rebound behind the net and scored on a wraparound.
The Rangers were the faster team throughout the game. They blocked 21 shots, had nine fewer giveaways than the Flyers, and had numerous good looks at Mason as they finished with a 38-25 shots domination.
But Mason stole the win, making this a best-of-three series.