The Lightning (51-19-4) lead the Atlantic with 106 points, six ahead of the Boston Bruins, who have two games in hand. Tampa Bay went 50-24-8 in 2014-15.
Coach Jon Cooper tied John Tortorella for most wins (239) in Lightning history.
[WATCH: All Lightning vs. Islanders highlights]
J.T. Miller scored twice, Brayden Point had a goal and two assists, and Anthony Cirelli, Tyler Johnson, Victor Hedman and Mikhail Sergachev scored for Tampa Bay.
Video: TBL@NYI: Sergachev rips slapper for power-play goal
"This is a good hockey team," Lightning captain Steven Stamkos said. "We've found a way to break a franchise record so that's pretty cool in itself but we've been saying for a while that it's a different feel this year. It's a feel where we think we have a team that can do some damage in the Stanley Cup Playoffs, so we'll continue to try and pile up the wins. We want to get in the playoffs and play a lot better than we have been."
Andrei Vasilevskiy made 35 saves to tie Nikolai Khabibulin for second place on the Lightning wins list with 83. It was his NHL-leading 42nd victory.
Ryan Pulock, Anders Lee and Anthony Beauvillier each scored twice, and Jordan Eberle had three assists for the Islanders (31-33-10), who are 10 points behind the New Jersey Devils for the second wild card into the playoffs from the Eastern Conference with eight games remaining.
"It kind of [stinks] the position we're in, but I'm just looking to improve every aspect of my game and have a strong finish," Pulock said. "Hopefully it will lead into next year."
Video: TBL@NYI: Cirelli, Johnson score 26 seconds apart
Miller scored his second of the game on the power play with 1:40 remaining in the second period, tapping in a pass from Nikita Kucherov to make it 7-3. The Islanders scored three goals in 3:01 during the third period to make it 7-6, with Lee scoring on the power play at 1:35 and Beauvillier scoring at 3:21 and 4:36, the latter a deflection of a Johnny Boychuk shot from the point.
"We have a skilled group of guys," Cooper said. "Miller has been a pretty good complement for Nikita Kucherov and Stamkos. He's a strong kid, wins most puck battles and has enough skill to play with those guys."
Lightning defenseman Ryan McDonagh blocked three shots in 21:34, including one by Pulock with 26 seconds remaining in the third.
"[McDonagh] is a graceful skater and can get around the ice, but you watch in the 6-on-5 when the Islanders pulled their goalie and the big blocks from him," Cooper said. "He knows when to jump into the rush and when not too, and he's a big stabilizing force back there."
Video: TBL@NYI: Point nets SHG for his 100th NHL point
Point scored shorthanded at 2:43 of the second period, finishing a 2-on-1 with Cirelli, to give the Lightning a 4-1 lead before Pulock scored a power-play goal at 3:20 and Lee scored at 5:15 to pull the Islanders within 4-3.
Miller scored at 8:27 of the second to give the Lightning a 5-3 lead, and Sergachev made it 6-3 with a power-play goal at 11:22.
Jaroslav Halak made 11 saves for the Islanders after replacing Christopher Gibson, who allowed six goals on 24 shots.
Cirelli (2:09) and Johnson (2:35) gave Tampa Bay a 2-0 lead in the first period, before Pulock scored on a 4-on-3 power play at 10:24 to make it 2-1. Hedman made it 3-1 at 14:17, scoring over Gibson's right shoulder on a wrist shot from the left face-off circle.
Goal of the game
Miller's goal at 18:20 of the second period.
Video: TBL@NYI: Miller buries Stamkos' pass on rush
Save of the game
Vasilevskiy's save on Chris Wagner at 8:17 of the second period.
Video: TBL@NYI: Vasilevskiy denies Wagner in the 2nd
Highlight of the game
Hedman's goal at 14:17 of the first period.
Video: TBL@NYI: Hedman picks the corner on Gibson
They said it
"When you look at the coaches over the last 10-to-15 years, John Tortorella has been a really good one. I spent time with the 2004 Tampa Bay Lightning team and they talk about [him] in extreme high regard. I'm fortunate to have met him a few times and know what he meant to our organization. He laid the groundwork here, so if my name is up beside John Tortorella's, I consider that an honor." -- Lightning coach Jon Cooper
"After the second intermission, all you want is some fight and hunger. We realized the shots were even (27-26 for New York) even though though it was a 7-3 game. We thought if we get one, maybe we could get going. We battled in the third but it wasn't good enough. It was nice to see the guys battle." -- Islanders coach Doug Weight
Need to know
Kucherov leads the NHL with 95 points (37 goals, 58 assists), one more than Edmonton Oilers center Connor McDavid (36 goals, 58 assists). … Stamkos has 32 points (10 goals, 22 assists) in his past 27 games. ... Cooper was hired March 25, 2013, but didn't coach and win his first game until four days later, a 5-4 shootout win against the New Jersey Devils. ... Islanders center Mathew Barzal, who has seven points (two goals, five assists) during a five-game point streak, got his 56th assist, the most in a season by a rookie since Pittsburgh Penguins center Sidney Crosby in 2005-06 (63).
Lightning: At the New Jersey Devils on Saturday (7 p.m. ET; MSG+ 2, SUN, NHL.TV)
Islanders: Host the Chicago Blackhawks on Saturday (7 p.m. ET; MSG+, WGN, NHL.TV)
Video: Lightning set club wins record in 7-6 victory