The Flyers have an unfamiliar edge on opponents. Carter Hart’s brilliant night against the Bruins proves it. | Mike Sielski

BOSTON — Afterward, Carter Hart considered the goal that the Boston Bruins — the defending Eastern Conference champions, perhaps the best team in the National Hockey League — had nearly scored against him, and he laughed.

This was in the second period Sunday night at TD Garden, when the Flyers still had the Bruins under control, before their legs got heavy from their second road game in two nights and before Hart had to make 15 saves in the third period and four more in overtime and a shootout in the Flyers’ 3-2 victory.

This was the first time that the Bruins tested Hart, a bad Justin Braun outlet pass turning into a Connor Clifton breakaway. Hart fended off Clifton’s shot with his left pad, then bodies came careening toward the net, a whistle blew, and Clifton lifted his hands to celebrate something that hadn’t officially happened. The referees waved their hands no. Goaltender interference.

“It was funny,” Hart said later in the locker room. “They thought it was a goal. I knew it wasn’t. It was just a guy who jammed my pad over the line.”

There was an amiable dismissiveness to Hart’s comments about the whole thing, the sort of reaction you might expect from any 21-year-old kid, even one already on his way to establishing himself as an elite NHL goaltender. A goal? I’m, like, dude, no way.

Hart carries himself as if he ought to make the kind of saves he made Sunday night: stoning David Pastrnak, the NHL’s leading goal-scorer, on a penalty shot, blocking back-to-back one-timers from Patrice Bergeron and Pastrnak on a late Bruins power play. He carries himself as if the Flyers ought to expect him to make those kinds of saves, too.

“Every guy in the room knew how good he played for us tonight,” said rookie forward Joel Farabee, who scored the Flyers’ shootout goal. “It happens every game. You’re going to have shifts where you’re stuck in the D-zone, and you’re kind of running around. When you’re running around and you know you’ve got a great goalie, it just gives you that confidence to just play how you’ve always played — to not panic, I guess. You don’t panic if you know he’s back there.”

It’s a powerful thing in this league, to have a goaltender who can do what Hart did Sunday night, in a game that approximated a playoff contest’s atmosphere and stakes as much any mid-November game can. The Bruins had lost their previous two games, and the Flyers had beaten the Maple Leafs in Toronto — in a shootout — less than 24 hours earlier.

“I’m interested to see how we respond,” Flyers coach Alain Vigneault said a couple of hours before the opening faceoff. “It’s a challenge.”

For two periods, the Flyers responded well to it. They’ve been a better team this season than they’ve been in recent years: deeper, more experienced and talented, better coached. But the third period and the extra sessions Sunday were a reminder of the difference that great goaltending can make, the difference that Hart can make if he continues to play like he has for most of this season.

His statistics aren’t as impressive as his play generally has been: an .893 save percentage, a 2.71 goals-against average. “You’re going to have ups and downs over your career,” he said, “and it’s important that you don’t get too high and you don’t get too low.”

He had an ugly three-game stretch last month, a predictable part of any young goaltender’s maturation as opponents scout him for soft targets, but he has righted himself. In his last three games, he has stopped 81 of 86 shots, and even on a night when the Flyers were excellent for two-thirds of regulation play, they still needed their goalie to steal them a point. Hart stole them two.

“A lot of times in these [back-to-back] games, you need him early on to let your legs get going,” Vigneault said. “Tonight, it was different. It was in the third period when we needed him, and he was huge.”

Understand: Brian Elliott has been healthy so far this season, and he has been excellent, but everyone knows the score here. Elliott is the veteran backup, the guy who should play 25-30 games during the regular season so that Hart can be sharp and fresh come the postseason. And if circumstances allow the Flyers to carry out that plan, they will make the playoffs — and once they get there, they should have an advantage that they haven’t enjoyed in more than a decade.

Think about it: When was the last time the Flyers entered a postseason series with the better goaltender? Not with a hobbled Elliott in 2018, not against the Capitals’ Braden Holtby in 2016 or the Rangers’ Henrik Lundqvist in 2014, not with the squirrelly Ilya Bryzgalov in 2012, not with Peter Laviolette’s carousel of goalies in 2011, certainly not with their deep defense corps covering for Michael Leighton during that run to the Stanley Cup Final in 2010.

How far back do you have to go? Martin Biron in 2008? Ron Hextall in 1987? The name doesn’t matter much. The fact that the question is worth asking matters more. For the Flyers, the fact that Carter Hart might answer it could mean everything.