Florida hadn't trailed by more than one goal in 10 straight games.
"We gave up a power-play goal, a shorthanded and two 4-on-4, which doesn't happen very often to give up two," Brunette said. "I think a little bit of our management ability in certain areas we talk about a lot, the blues and just inside the blue, we just weren't completely sharp at different times in the game when we needed to be."
Kreider scored his team-leading ninth goal and NHL-best sixth on the power play at 7:52 of the first period, one minute after Shesterkin stopped Frank Vatrano on a breakaway.
"You can see it in the game how much energy we get from him," Miller said of Shesterkin.
Fox made it 2-0 with his shorthanded goal at 19:54 of the first period.
Sam Reinhart joined teammates Jonathan Huberdeau and Aaron Ekblad in pursuit of Barclay Goodrow, the puck carrier. That left the middle lane for Fox, who took the pass from Goodrow and skated through the open space to the net before beating goalie Spencer Knight (14 saves).
"I mean, there's less than 10 seconds left and in my mind I think I got too puck-focused," Reinhart said. "There's no need for me to go in there. I'm not going to turn the puck around and get an opportunity on the other end, so I think we just cut our losses at that point."
Panarin had a goal disallowed because of goalie interference at 9:10 of the second.
The Panthers challenged because Strome was in the crease, blocking Knight's ability to play his position by getting across to stop Panarin's one-timer from the right circle.
"He went in unobstructed, so I thought it was the right time to challenge and I felt pretty confident," Brunette said.
The Rangers made it 3-0 at 12:48, when Miller scored on an end-to-end rush.
Gallant joked that he'd turn the second-year defenseman into a left wing after seeing the rush.
"It was an incredible goal," Gallant said. "He's got a lot of talent. You see his raw skill and his talent. He can skate and he's got that big reach. It was really nice to see, a good confidence-builder for him."
Strome scored on a one-timer off a pass from Panarin at 13:18 to give New York a 4-0 lead.