Martone also had an assist, and Dvorak had a goal and an assist for Philadelphia (39-26-12), which is 14-6-1 in 21 games since the break for the 2026 Winter Olympics. Dan Vladar made 18 saves.
It's the first time the Flyers are in a playoff spot since Jan. 12. They are one point ahead of the New York Islanders, who have played one more game, and two points ahead of the Columbus Blue Jackets.
"There's a lot of growth," Philadelphia coach Rick Tocchet said. "I think the team's done a great job since training camp. A little bit of a roller coaster sometimes, but for the most part, this team has stuck together all year. Really proud of them."
Pavel Zacha scored and Korpisalo made 29 saves for Boston (43-26-9), which has lost three straight, including 3-1 at the Tampa Bay Lightning on Saturday.
The Bruins hold the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
"A huge point for us," Bruins coach Marco Sturm said. "Guys battled back. We wanted to have a power-play goal in the third and we did. 'Korpi' made some great saves. Unfortunate there in OT, but we'll definitely take that point."
Martone did his own setup work on Dvorak's goal that gave the Flyers a 1-0 lead at 4:19 of the first period. He played a puck off the boards between his legs to send Dvorak and Travis Konecny off on a 2-on-1 rush. Dvorak kept the puck and snapped a shot past Korpisalo's glove from the right face-off circle.
"Not an easy play at all," Dvorak said. "And straight on my tape, I (didn't) even have to move my stick. A high hockey IQ play. Very smart player. Those are big plays and he was a massive difference maker for us tonight.
"He's a confident kid, confident player. And that's what you need in this League. So it's been fun to watch, fun to play with him. And he's only going to get better."
In four games since his debut March 31, Martone has three points (one goal, two assists) and leads the NHL with 20 shots on goal.
"Awesome," Flyers forward Noah Cates said. "He's helped us. That's the biggest thing this time of year, and especially for a younger kid, to come in and help us, bring energy. It's huge for us. For him to keep going and get one and get confidence, it's been big for us."