Rookie Michael Grabner netted his 30th goal, Micheal Haley and Parenteau also scored in regulation, and DiPietro finished with 29 saves through overtime for the Islanders, who snapped a six-game skid on the road.
"I felt pretty good," DiPietro said. "There's obviously a little bit of rust you have to shake off after six weeks but I was pleasantly surprised with how well the communication and the handoffs with the defense went."
Parenteau made sure he didn't miss his chance to win the game.
"I just came left with a little bit of speed and I went to my go-to move and it went over his glove," Parenteau said. "It's a move that's been working for me lately."
Dadonov notched his first NHL multigoal game in his first game since he missed 20 because of a broken finger.
The Panthers tied it at 3 on Weiss' goal at 13:26 of the third period. His slap shot from the top of the right circle got past DiPietro's glove.
"I don't usually let that [third] goal in, and the team played so well it would have been nice to win it in regulation," DiPietro said.
New York scored two goals on just four shots in the third period.
The Islanders took a 3-2 lead when Haley took the puck in his zone, skated to the net and put a wrist shot between Clemmensen's pads at 9:50.
New York tied it 2-2 at 7:09 of the third when Parenteau took a pass from Jack Hillen in the slot and beat Clemmensen on the stick side.
Dadonov's second goal gave the Panthers a 2-1 lead at 17:28 of the second.
"I wasn't very lucky defensively ... being on the ice for all three [Islanders] goals," Dadonov said. "It's pretty hard to come back after 20 games. I'll try and get better. I knew exactly what I had to do [defensively] but I can't do it. My brain was doing other things."
The Islanders took a 1-0 lead on Grabner's short-handed goal at 5:14 of the second.
Dmitry Kulikov turned the puck over in the Islanders zone, and Grabner skated the other way. Grabner fed a pass above the right circle to Nielsen, who gave the puck back to Grabner. His shot from the left circle got past Clemmensen and gave him a tie for the team lead in goals with Matt Moulson.
Grabner leads NHL rookies in goals.
"It was a big win after going into the third period down 2-1, but we battled back and in the end we got the win and that's all that matters," Grabner said.
Florida tied it at 1 on Dadonov's goal in the second period, but the Panthers absorbed their 27th one-goal loss this season.
"Disappointing. You go in the third with a 2-1 lead, give up four shots, have a penalty shot in overtime with a chance to win it and end up losing the game," Panthers coach Peter DeBoer said. "I thought we deserved better but you have to give the Islanders credit. They're opportunistic."
DiPietro missed 20 games after sustaining broken facial bones during a fight with Pittsburgh goalie Brent Johnson on Feb. 2. DiPietro also had an injured knee. ... The Islanders are 1-7-1 at Florida since a 4-1 win Nov. 18, 2006. ... Grabner has five goals and four assists in nine games. ... Panthers D Alexander Sulzer missed his seventh game due to a strained oblique.