The Rangers were given their third power play -- the only ones in the game --just seconds into the extra session, and Marian Gaborik ended his long scoring drought to give them a 2-1 win at 42 seconds of overtime.
"We didn't quit. We kept working it," said Gaborik, who scored for the first time in nine games.
The Rangers have won a season-high four in a row, and had plenty of supporters at Nassau Coliseum cheering them on despite being on enemy ice.
Nash again showed that the third period is his favorite time, scoring his eighth of the season -- all in the third -- and assisting on Gaborik's winner.
Since he missed four games because of injury, all losses by the Rangers (0-3-1), Nash has five goals and three assists in four games. He has an eight-game point streak, and the Rangers are 11-2-1 when he has a point and 12-5-1 when he plays.
"The great part about Nash right now is his third periods are his best periods," Rangers coach John Tortorella said. "He's been a huge part to our club as advertised. He has been a game-breaker for us, and hopefully that will continue.
"He doesn't speak, he just goes out and plays."
Gaborik took a feed in the high slot from Nash and fired in a shot for his eighth of the season.
The Rangers earned the power play when Michael Del Zotto was hauled down as he crashed in on Islanders goalie Evgeni Nabokov 21 seconds into overtime.
When the winning goal was scored, the Islanders were irate and complained to the officials before leaving the ice. A handful of insignificant misconducts were assessed to the club.
"I felt like it was a pretty easy call," Del Zotto said. "A penalty is a penalty, regardless of what time of the game it is, especially a Grade-A scoring chance like that. If it takes away from an opportunity it has to be called."
Henrik Lundqvist made 27 saves for the win. Nabokov stopped 35 in a tough-luck loss.
"I am pleased with the effort," Islanders coach Jack Capuano said. "We were 5 minutes away."
Right after the Islanders used their timeout late in regulation, the Rangers broke through on Nabokov with their 32nd shot. Derek Stepan kept the puck in at the left point and sent a drive that Nash deflected in.
That evoked cheers and chants of "Let's Go Rangers" that increased when Gaborik won it.
Until the Rangers' late flurry, Michael Grabner's first-period goal stood up for the Islanders.
"This was a big one," Lundqvist said of the win. "I just kept telling myself, 'I need to stop the next one.' Great atmosphere in this building. It's always fun to play here."
He couldn't keep Nash down for good.
Staal sat out for the first time this season because of injuries sustained Tuesday when he was struck in the right eye by a deflected puck in a victory over Philadelphia. Staal is out indefinitely, but doctors are optimistic he will make a full recovery.
The Rangers held a 13-12 shots advantage in the first period, but the Islanders grabbed the early lead. After creating a couple of early chances with his speed, Grabner scored with 8:09 left in the first period. He was set up in the middle of the slot when Colin McDonald found him with a pass from behind the net. Grabner fired a rising shot that beat Lundqvist to the upper right corner of the net for his 10th goal.
Grabner has scored in three straight games and four of seven. He nearly netted another just more than three minutes into the second period when he got free on a rush and fired an unimpeded drive from the left circle that Lundqvist blocked aside.
The Rangers received two power plays in the second period, but did little with them. The Islanders had the best chance when Matt Martin got free for a short-handed breakaway, but his in-close drive was knocked away by Lundqvist with 3:45 left.
Richards missed his second straight game because of neck and back soreness following a hit into the boards from behind on Sunday. ... Veteran D Roman Hamrlik, formerly of the Islanders, made his Rangers debut one day after being claimed off waivers from Washington. ... Islanders LW Eric Boulton played in his eighth game of the season, and second since Feb. 14 against the Rangers, in place of David Ullstrom. D Lubomir Visnovsky missed his second consecutive game because of personal reasons. ... Grabner became the Islanders' third double-figure goal scorer, joining John Tavares (14) and Matt Moulson (11). The Rangers don't have any. ... The Islanders dropped to 0-10-1 when they score fewer than three goals. They are 1-7-2 when Tavares fails to record a point. He has been held off the sheet in four of five games.