Brome gave Detroit a 2-1 lead at 17:27 of the second on a rebound. It was his first NHL point in his 18th game.
"I'm old enough to know things will get better as long as you are creating chances," the 26-year-old said. "My first year in Sweden, I didn't have a point for 14 or 15 games, so I've done this before. It was frustrating, but I would have only worried if I wasn't creating chances."
The Panthers generated 14 shots in the second period, but forward Frank Vatrano said the Red Wings outplayed them.
"I thought we had a flat second period," he said. "Obviously, they were the hungrier team after what happened yesterday, and when you take a period off, this is what happens."