Dawson Mercer tied it 1-1 on a one-timer at 11:25, and Hughes put the Devils ahead 2-1 from the left side of the net at 15:16.
The Red Wings attempted to challenge the goal, claiming Devils forward Erik Haula had interfered with Nedeljkovic, but didn't ask for the review quickly enough.
Bratt made it 3-1 on the power play, knocking in Hughes' pass 43 seconds into the second period. It was the first power-play goal allowed this season by Detroit, which had killed off its first 17 penalties.
"Jack's been playing really well, and we've spent a lot of time working on the power play," Bratt said. "He loves to get me the puck on the back door, so I'm always going to be ready for that pass."
Yegor Sharangovich extended the lead to 4-1 at 4:54 with a shot from the right circle for the fourth short-handed goal of his NHL career (137 games).
"He does a really good job out there, especially with his reads, and that shot was a bullet," Ruff said.
Kubalik cut it to 4-2 at 8:17 of the third period.
Nico Hischier made it 5-2 when he spun and scored in front at 15:38, and Bratt scored from the left face-off circle on the rush at 16:27 for the 6-2 final.
"We had a good start, but I think we let the game turn into a turnover fest, and that's the way they want to play," said Larkin, the Red Wings captain. "They turn over pucks too, but they made us pay on our turnovers. We were just sloppy all night."