Flyers 3, Winnipeg 2.
"That's why he's our captain, I think," winger Wayne Simmonds said of Giroux. "I don't think. I know.
"G's an extremely competitive guy and someone everybody in this room looks to in big moments," winning goalie Steve Mason said.
Returning home after a four-game road trip, the Flyers remained in the final Eastern Conference wild-card spot.
They stayed tied with Detroit, which eked out a 3-2 win over visiting Buffalo, in the wild-card race. The Flyers are technically ahead, however, because they have played one fewer game.
After getting the game's first seven shots and dominating the opening minutes, the Flyers started to fade, perhaps fatigued from the long road trip. They returned from Arizona on Sunday.
"Maybe physically we weren't there, but I think mentally we took care of pucks," Giroux said.
On the game-winning sequence, Gostisbehere said it was worth the risk to keep the puck in the zone, even though the Jets would have had an odd-man rush if he wasn't successful.
"I'll take his calculated gamble any time," said Simmonds, whose team was not shorthanded in a game for the first time since 2012. "He's generally pretty good when he's doing things like that."
Said Gostisbehere: "It was more desperation than anything. I probably wasn't going to get back. Gaggy [Sam Gagner] just said, 'Thank God you got that because I don't know what I would have done with a three-on-one.' "
After he scored, Giroux lifted his arms skyward, like a football referee signaling a touchdown.
"I was too tired to celebrate, so I just threw my arms in the air," he said.
Gostisbehere nearly won it late in regulation. After making a great move to get free for a shot, he fired a drive that bounced off the crossbar with 5 minutes, 38 seconds to go.
Blake Wheeler took a slick pass from Scheifele and beat Mason on a backhander with 17:25 left in regulation, knotting the score at 2-all.
Mason, making his 11th start in the last 12 games, kept the game tied when he stopped Nikolaj Ehlers from point-blank range with 11:31 remaining.
Earlier, Mark Streit and Simmonds scored on the Flyers' first two shots of the second period to create a 2-0 lead.
But 78 seconds after Simmonds' goal, Scheifele scored on a breakaway as he beat Mason to the short side. A turnover by Jake Voracek enabled Scheifele to go in alone and score his 25th goal.
Just 41 seconds into the second period, Streit converted a backdoor pass from Sean Couturier to give the Flyers a 1-0 lead. Simmonds then scored from the high slot - his wrist shot caromed off the leg of defenseman Dustin Byfuglien and past Pavelec - after taking a pass from Brayden Schenn, who was behind the net.
"I just came off the bench and shot it," Simmonds said after scoring his 26th goal, tops on the team.
As expected, Giroux was able to play after absorbing a head hit Saturday in the 2-1 loss in Arizona. Giroux, the Flyers' leading scorer, went through a concussion test and doctors cleared him.
"I was a little shaken up, but [after] getting the rest, I feel pretty good," Giroux said after watching Monday's morning skate. ". . . I feel fine. I don't think there was a question of me playing tonight or not."
Giroux finished with two points, five shots, and a 61 percent success rate on his 18 faceoffs. He tied Reggie Leach (514 points) for 12th on the all-time franchise list.
Gostisbehere said he was a little concerned Giroux might not be able to play.
"But he told us the whole time he was good and you have to trust him - and it worked out tonight," he said.