Hornqvist pushed it to 4-0 at 18:13 of the first with a shot from a sharp angle that redirected in off Sorokin's mask. Aaron Ekblad then made it 5-0 at 13:41 of the second period with a slap shot from the right circle.
Palmieri scored his first of the season to make it 5-1 at 15:00.
"There's no time to feel sorry for ourselves," Palmieri said. "Nobody's going to give us an easy out. It's going to be us playing and clawing our way back."
Frank Vatrano scored on a 2-on-1 at 16:36 of the third period for the 6-1 final.
"We're definitely upset with our play, there's no doubt about it," Islanders center Casey Cizikas said. "We take a lot of pride in who we are and how we play. It's not easy, but we'll be upset about this tonight, get home and get the body ready, and be ready for that home opener now."
NOTES:Florida is 8-0-0 at home this season. … Prior to the game, the Islanders announced that defenseman Ryan Pulock would miss the game because of a lower-body injury and would be evaluated once the team returned to New York. They also announced that center Josh Bailey had entered COVID-19 protocol. … Florida's win was the 900th in its history. … Bobrovsky (7-0-2) is the second goalie in Panthers history to begin a season without a regulation loss through his first nine games, joining John Vanbiesbrouck (6-0-3 in 1996-97). … This is the first time that the Islanders have allowed at least four goals in four straight games since hiring Trotz prior to the 2018-19 season.