After Nelson gave the Islanders a 1-0 lead with a snap shot from the left face-off circle at 11:27 of the second period, Coleman took a lofted pass from Yanni Gourde and scored 15 seconds later on a breakaway to tie it 1-1 at 11:42.
Following the ensuing face-off, Kucherov skated in on a rush and sent a cross-slot pass to Palat for a one-timer to give Tampa Bay a 2-1 lead at 11:54. Palat has eight goals in the postseason, with each coming in the past eight games.
"You want to follow up a goal with a good shift and kind of stay on it," Nelson said. "They had a better response than we did, and that was the difference, really. Thirty seconds there. If you can hang on, it's a different game."
Point extended the lead to 3-1 at 3:33 of the third period, tapping his own rebound into an open net after his initial attempt following a cross-crease pass from Palat hit Varlamov's skate.
Kucherov and Point had the assists on Palat's goal, and Palat and Kucherov had the assists on Point's.
"Their first line put a mark on us in a couple of game here," Islanders coach Barry Trotz said. "They're all good players. They're outstanding players. They can make plays. They go to the hard areas. ... They're high-level, elite players. You can't give them an inch. We've given them too many inches."
Pat Maroon scored an empty-net goal with 2:24 remaining for the 4-1 final.
In addition to Point, Lightning forward Alex Killorn also returned after serving a one-game suspension in Game 3 for boarding Nelson in Game 2. He had three hits and two blocked shots in 18:21 of ice time.
NOTES:New York forwards Casey Cizikas and Tom Kuhnhackl each left the bubble because of an undisclosed injury and will not return for the remainder of the playoffs. … New York was 0-for-3 on the power play and has scored once on 14 chances in the series. … Tampa Bay has won seven of its past eight games since losing 3-2 to the Bruins in Game 1 of the second round on Aug. 23. ... The New Jersey Devils rallied from down 3-1 to defeat the Philadelphia Flyers in the 2000 Eastern Conference Final and then won the Stanley Cup.
NHL.com staff writer Mike Zeisberger contributed to this report