Bratt went behind the net and snuck a wraparound inside the right post, before defenseman Mike Matheson could poke it away, for his second goal of the season.
"Think we played much harder as a group," Bratt said. "We wanted to win. That was something that mirrored our game today. We wanted to compete, and we wanted to win this game really bad. That's how it should be. ... Overall, it was a great performance by all the four lines."
Mackenzie Blackwood made 35 saves in his return after missing two games with an upper-body injury, and Sami Vatanen scored for the Devils (11-14-4), who have won three of four games.
Tristan Jarry made 33 saves, and Sidney Crosby scored for the Penguins (19-11-2), who have lost three of four since a six-game winning streak.
"We're playing a lot of games here. We just went through a stretch where we played an awful lot of hockey (five games in seven days)," Pittsburgh coach Mike Sullivan said. "So that's one of the challenges in this particular circumstance in this year with the condensed schedule. So we've got to get contributions throughout our lineup if we're going to get consistent results.
"We're getting consistent offensive production, obviously, from Crosby's line. But it would help if we could get some more from the bottom nine. So that's one of our challenges right now."