Poti, a defenceman who assisted on two other goals, snapped a shot from inside the blue line that passed through a screen by Mike Sillinger and found the net behind John Grahame.
It gave Rick DiPietro his first win of the season following a four-game layoff due to a groin injury.
Carolina suffered its second straight tough loss and concluded a season-high, seven-game road trip. The defending Stanley Cup champions took a while to find their legs following a fast-paced 5-4 defeat at Buffalo on Friday night, but they nearly pulled this one out with three third-period goals.
After Jason Blake and Mike York staked the Islanders to a 2-0 lead, the Hurricanes stormed back to take the lead. Justin Williams scored short-handed and power-play goals 1:50 apart, and captain Rod Brind'Amour made it 3-2 with 5:26 left in regulation.
But it didn't stand up as Sillinger tied it for the Islanders with a power-play goal at 16:50.
DiPietro, playing at home in the regular season for the first time since signing a 15-year deal with the Islanders, fought the puck early on but regrouped in the final two periods. He couldn't be faulted much for the Hurricanes' late uprising that nearly cost New York a victory.
Instead the Islanders snapped a two-game losing streak, while playing into overtime for the fourth time in five games.
While New York celebrated this win, Carolina defenceman Mike Commodore watched in dismay from the penalty box. He looked up at the scoreboard to see that 34 seconds still remained on his holding infraction that decided the game.
DiPietro finished with 37 saves in his first outing since yielding four goals on 40 in shots at Los Angeles - a defeat that made the 25-year-old goalie 0-3.
Grahame, a U.S. Olympic teammate of Blake and DiPietro at the Turin Games, made his second start since joining Carolina in the off-season.
Until the Islanders' rally he was enjoying a much better performance than his Hurricanes debut when he allowed six goals on 31 shots in a 6-3 loss at Florida on Oct. 11.
He gave up four goals on 25 shots.
Notes: Mike Dunham went 2-0-2 while filling in for DiPietro. ... Hurricanes G Cam Ward, the MVP of last season's playoffs, served as the backup after starting four straight games. He gave up all five goals in Friday's loss at Buffalo. ... Along with Blake, DiPietro and Grahame, Carolina D Bret Hedican and LW Erik Cole were members of this year's U.S. Olympic team. ... The Hurricanes went 4-3 on the trip.