Okposo, whose sharp passing set up the Islanders' first two goals, scored 4:13 into overtime and lifted his team to a 3-2 victory that snapped the New York Rangers' four-game winning streak Saturday night.
It was a long time coming for Okposo, who had five goals in his first 19 games but none in the next 18.
"It felt like a pretty big relief. To get the win that way, it felt pretty good," said the 21-year-old Okposo, who hadn't scored since Nov. 14. "I've played pretty well. I think I've been playing like that for quite some time, but the puck was just not going my way. Tonight it did."
Okposo, whose three points were a career high, earned primary assists on goals by Frans Nielsen and Blake Comeau and then fired a drive from the blue line that caromed off Rangers defenseman Marc Staal and then the post before beating Henrik Lundqvist. Dwayne Roloson made 36 saves for the win.
It didn't appear that overtime would be necessary to settle the third meeting in 11 days between the rivals, but Brandon Dubinsky scored twice in the third period, including the tying tally with 46.6 seconds left to give the Rangers a standings point.
Dubinsky, who brought the Rangers to 2-1 at 6:07, then deflected Ryan Callahan's shot past Roloson for his sixth of the season and third in seven games since returning from a hand injury.
But the Rangers couldn't complete the comeback in the extra session.
"It makes it a little harder," Dubinsky said. "Your juices are flowing, you've got the momentum, you're excited about tying the game and getting a point. You want to fight to get that second one and use that energy.
"We had some chances, but unfortunately they found a way to get one past Hank."
The Islanders had led for all but 7:45 before Dubinsky tied it. The Rangers had 15 shots in both the second and third periods, compared to 14 total for the Islanders in the final 40 minutes of regulation. The shots were 3-3 in overtime.
"Obviously huge for Kyle and a big goal for us," Islanders coach Scott Gordon said. "They were going pretty good in the third period, and I like the way our guys responded in overtime. They found a way to get that second point."
The Rangers carried play and finished with a 38-22 shots advantage. But the Islanders earned their third victory of the season over the Rangers in four chances. Last season, the Islanders lost five of six matchups.
"Anytime you play your own division, you want to get wins so it's definitely important in that aspect," Okposo said.
Okposo assisted on Nielsen's even-strength goal in the first and on Comeau's short-handed score in the second for the Islanders, who have won two straight and four of 11.
An Islanders penalty for too many men gave the Rangers a power play with 3:17 left, but the Rangers finished 0 for 3 with the advantage. The Islanders had allowed 16 goals in their previous 37 short-handed situations.
The Rangers hadn't lost since a lifeless 2-1 defeat to the Islanders on Dec. 16 that started a home-and-home series. That defeat led coach John Tortorella to bench defenseman Wade Redden and forward Ales Kotalik for two games, and drop captain Chris Drury to the fourth line.
"Believe it or not, I think the athletes cared," Tortorella said. "I thought we were embarrassed in our building last time. Obviously, that kicks up a little dust in meetings, in talks among the team."
The Islanders took a 1-0 lead on their second shot. After Rangers defenseman Dan Girardi flubbed a drive at the blue line, the puck was cleared down the ice. Josh Bailey got to it, and he fed a pass in front. Okposo corralled the puck near the right post and made a behind-the-back pass to Nielsen, who knocked in his sixth goal.
The Rangers had a chance to take advantage of the Islanders' struggling penalty-killers after defenseman Brendan Witt went off for hooking Ryan Callahan during a rush. But instead of getting even, the Rangers' deficit doubled with 5:39 left in the second.
Okposo eluded hits along the right-wing boards by Michael Del Zotto and Kotalik and feathered a pass in front to Comeau, who slipped a shot between Lundqvist's pads. The short-handed tally was Comeau's fourth goal and second in two games.
"I was too aggressive," Lundqvist said. "When he stopped in front of me, I tried to check him and I opened up. ... I made the first move and I lost."
Lundqvist made his 24th straight start against the Islanders, dating to Dec. 26, 2006. The Islanders have used five goalies against the Rangers in that span. ... The Islanders have scored four short-handed goals this season. The Rangers have allowed four, including three in eight games.