Kevin Rooney pushed it to 3-1 at 2:55 of the third period on a shot from the slot. It was his first goal since Dec. 7, 2021.
Hischier cut it to 3-2 at 4:02 with a short-handed goal on a breakaway.
"We have to be stronger in front of our net," said Hischier, the Devils captain. "We had our chances, but we didn't bear down so it's frustrating for sure. But there's still a lot of hockey left."
Kuzmenko made it 4-2 at 9:56 on a turnaround shot from the high slot. It was Kuzmenko's second goal in his second game with the Flames since being acquired in a trade with the Vancouver Canucks on Jan. 31.
"The one thing that I've noticed over the last couple of games is he's heavy and strong on it, so he's able to protect it," Huska said. "He can spin off guys, and when he gets a chance to shoot, he's got an excellent shot."
Palat cut it to 4-3 at 13:46 with his second goal, scoring on a deflection at the left post.
Mangiapane scored into an empty net at 18:26 for the 5-3 final.
"In the second period, we just came out like a pack of hyenas," Calgary forward Jonathan Huberdeau said. "That's the kind of game we have to play. I think that's when we're tough and we have to keep it going because it's a huge road trip for us."
NOTES: The Flames have won the first two games of a four-game road trip. ... Yegor Sharangovich, who played the first three seasons of his NHL career with the Devils, received a video tribute and ovation from the crowd in his first game back at Prudential Center with the Flames. The forward had one shot on goal in 16:07 of ice time. ... Huberdeau played his 800th NHL game, becoming the fifth player from the 2011 NHL Draft to reach the milestone (Ryan Nugent-Hopkins, 847 games; Brandon Saad, 830; Mika Zibanejad, 817; Adam Larsson, 817). ... Bratt extended his point streak to six games (nine points; four goals, five assists).