Noah Cates scored, and Hart made 20 saves for the Flyers (20-21-9) who have lost three straight (0-1-2) but have at least one point in 11 of 15 games (9-4-2).
"This was a game of two willing teams," Philadelphia coach John Tortorella said. "That's a hard team, hard building to play in. Happy we get a point, but it leaves you wanting more. Same type of situation, we go down and have a great chance. We don't score. They come right down and score on us.
"We're trying, but I respect how we played. I respect how they played. It was a hard-fought game."
Cates gave the Flyers a 1-0 lead at 5:14 of the first period when Rasmus Ristolainen's shot deflected off Cates and got past Fleury.
Boldy tied it 1-1 at 3:39 of the second period. He found a pass from Marcus Foligno that got caught up in Cam York's skates and shot it past Hart for his 15th goal of the season.
Boldy then put Minnesota ahead 2-1 at 4:48 of the third on the power play after cutting across the slot and redirecting a pass from Kirill Kaprizov.
"It was a good game for everyone," Boldy said. "I think it's the game we needed to play. Hard. Ended up being kind of a close one, back and forth, but yeah, I think it was a big game for us and a lot of guys played really well."