Balinskis scored his first goal of the season to give the Panthers a 1-0 lead at 12:14 of the first period, sending a point shot into traffic that beat Rittich gloveside.
Verhaeghe made it 2-0 at 7:05 of the second period. Florida defenseman Jeff Petry poked away a New York clearing attempt and Verhaeghe sent a one-timer through from the left circle.
The forward has four goals and an assist on his three-game goal streak.
The Islanders cut their deficit to 2-1 at 9:03. Barzal put a backhand shot at the net, and the puck glanced off the leg of Florida defenseman Gustav Forsling then went underneath the pad of Tarasov.
“It definitely was not our best,” defenseman Adam Pelech said. “They did a good job of checking, rimmed a lot of pucks and they came hard. Maybe we didn’t break it out well enough, and when we did get it stopped in the defensive zone, we didn’t break it down well enough from there, either.’’
Jones gave Florida a 3-1 lead at 13:57 of the third period during 4-on-4 play. Florida center Anton Lundell brought the puck up with speed, feeding Jones in the right face-off corner as he crashed the net. Jones sent a hard wrist shot over the glove of Rittich.