Florida had 20 blocked shots, including nine in the third period, when Bobrovsky made 13 saves.
"We just believed in ourselves," Panthers captain Aleksander Barkov said. "I know it probably didn't look pretty when they had chances to tie the game, but we battled hard. We tried to play the right way and I know they got a couple power plays at the end, so we tried to defend hard.
"The boys blocked the shots and 'Bob' was unreal in net."
Jesper Bratt and Erik Haula each had a goal and an assist for the Devils (1-1-1), who scored three straight goals in the third period. Michael McLeod scored, and Vitek Vanecek made 25 saves.
"Sometimes you won't score, but the numbers right now for generating aren't high enough in those first two periods," New Jersey coach Lindy Ruff said. "I thought they outskated us. I thought on the 50-50 compete, they won more battles than us."
Reinhart gave Florida a 1-0 lead at 3:54 of the first period when he scored on a deflection from the slot.
Verhaeghe pushed it to 2-0 at 13:12 when he scored on a backhand at the right post after taking a pass from Tkachuk and skating past defenseman Brendan Smith in the right face-off circle.
Mikkola made it 3-0 at 11:18 of the second period when he scored at the left post on a backdoor pass by Tkachuk from the bottom of the right circle.
"That was an elite pass from [Tkachuk]," Mikkola said. "I almost missed it, but it was pretty easy for me."
Ruff said, "I thought our defensive-zone coverage on the first goal was terrible. The one where they went to the net on the two defensemen was terrible. It's an area we have taken a lot of pride in, but there was not a lot of pride in some of our coverage and the desperation we need."