Mathieu Joseph tied it 1-1 at 3:16 of the first when he intercepted a pass from Sebastian Aho and beat Varlamov with a wrist shot to the glove side.
"I thought we needed a good shift," Joseph said. "Pretty good bounce in the middle of the zone. I had some time and space and tried to shoot it. I thought it was good to get that first goal back."
Anthony Cirelli put the Lightning ahead 2-1 at 19:22 of the first after he took control of a rebound and scored off the far post.
Cirelli provided a spark when he fought New York forward Brock Nelson at 12:56 of the second period after Nelson was called for charging Tampa Bay forward Alex Killorn. Cirelli and Nelson each received a major for fighting, and Cirelli got 10-minute misconduct and two-minute instigator penalties.
"What did he play, like nine minutes?" Lightning coach Jon Cooper said. "And he had the biggest impact in the game in nine minutes. That was a huge goal for us ... it wasn't a power-play goal technically, but he hung in there and made a great play. And then to stick up for a teammate like he did."
Point extended the lead to 3-1 at 13:28 of the third period after he gathered a loose puck in front of the net and scored from the low slot. Steven Stamkos made it 4-1 with a power-play goal at 15:30 of the period.
"I thought we came out, we got the first goal and we gave it back real quick ... way too quick," Islanders coach Barry Trotz said. "You want to take some momentum ... build some momentum, you score and they got it right back."