The Hurricanes were 2-for-6 on the power play, and the Lightning were 0-for-4.
Coleman gave Tampa Bay a 1-0 lead with a tip-in off a shot from Jan Rutta at 3:12 of the first period.
Maroon made it 2-0 at 5:41 when he scored off a pass from Ross Colton in front of the net.
"[Penalties] killed us tonight," Maroon said. "But there's a reason why we took penalties. They were better than us. They were down 2-0, but they stuck with it … we're the ones that got frustrated.
"We've just got to get back to our game. It's been an up-and-down roller coaster these last few games. We're in a good situation right now. We've been winning some hockey games as of late, so we've just got to stick with the structure and we'll be fine."
Cedric Paquette scored for Carolina to make it 2-1 at 2:24 of the second period, beating Vasilevskiy 1-on-1 off a pass from Necas.
"I don't play [Paquette] that much, probably could play him more," Brind'Amour said. "But every shift he goes out there, he gives everything he has. Great teammate. The guys really appreciate how he plays."
Sebastian Aho tied it 2-2 when he finished off a 3-on-1 rush in front of the net at 3:26.
Necas put the Hurricanes ahead 3-2 with a power-play goal at 15:44 when he scored off a loose puck that bounced off Aho's skate.
"Both teams played hard, and the games are intense," Aho said. "Obviously, the farther the season goes, every game is huge, and that's the defending champs. … It was quite a challenge for us. But I'm proud of how we responded when they were up 2-0. It was a great team effort."