It was the second-longest winning streak in Islanders history; they reeled off 15 consecutive victories from Jan. 21-Feb. 20, 1982.
Casey Cizikas and Cal Clutterbuck each scored for a second straight game, and Adam Pelech had a goal and an assist for New York (11-3-1), which was 10-0-0 when scoring at least three goals and 48-2-2 since Barry Trotz became coach at the start of last season. Semyon Varlamov made 35 saves.
[WATCH: All Penguins vs. Islanders highlights]
"We've held a lot of leads over the last two years," Trotz said. "We got passive and they got a push. … Bad on us. We needed everybody to make sure we did all the right things, get it deep, manage the puck, keep our shifts short, win the battles, races, all that."
Jared McCann had a goal and two assists for Pittsburgh (9-6-1), which tied the game with three straight goals in the third period. Matt Murray made 20 saves.
Video: PIT@NYI: McCann strikes from top of circle
The Penguins outshot the Islanders 26-14 over the second and third periods.
"I give our players a lot of credit," Penguins coach Mike Sullivan said. "Their resilience … to keep fighting and keep pushing in that third period I just think is an indication of the character we have in our room."
Rust won it for Pittsburgh when he stole the puck from Brock Nelson behind the Islanders net and beat Varlamov on a wraparound.
"I think all three of us were forechecking hard, just trying to get on them and get sticks on pucks and forecheck, and we were to cause a turnover," Rust said. "I just took it to the net."
McCann started the Penguins rally at 1:38 of the third period with a wrist shot from beyond the right circle that found its way through traffic to make it 3-1.
Rust extended his point streak to five games at 6:16 with a wrist shot from the right circle to make it 3-2. The goal came moments after Murray got his left pad on Anthony Beauvillier's chance from point-blank range.
Video: PIT@NYI: Rust scores after Murray's big save
"That's obviously a big moment, because they come around and score 15, 20 seconds later," Pelech said. "But it was an outstanding save by him. He's a good goalie. Good goalies are going to make those saves sometimes."
Evgeni Malkin then tied it 3-3 at 8:48 when he put a rebound past Varlamov after McCann's shot from the point hit the crossbar.
Trotz used his timeout after the goal.
"We were out-chanced probably 10-1 in the third period," Trotz said. "We were hanging on. That's not like us. Usually we're pretty good that way. We'll just learn from that."
Cizikas gave the Islanders a 1-0 lead 19 seconds into the game. Ryan Pulock sent a wrist shot from the right point that bounced off the boards behind the net to Cizikas at the far post, where he roofed a backhand shot over Murray.
Clutterbuck scored the Islanders' second shorthanded goal in as many games at 6:28 of the second period when he won a puck battle along the boards in the neutral zone against Jake Guentzel, skated into the slot and put a wrist shot past Murray to make it 2-0.
Video: PIT@NYI: Malkin cleans up rebound to tie it in 3rd
Pelech made it 3-0 with a one-timer from the blue line for his first of the season at 9:26 of the second.
It was the first game between the teams since the Islanders swept the Penguins in the Eastern Conference First Round of the Stanley Cup Playoffs last season.
"We played a good 40 minutes," Islanders captain Anders Lee said. "We didn't stick to what we had done through this stretch here, playing that full 60, putting teams away and not really letting them have an opportunity.
"We've just got to play better. That's not the way we've been playing. We all know that, that's why it's just a little bit frustrating."
Video: PIT@NYI: Murray thwarts Beauvillier with the pad
They said it
"If that doesn't happen, I don't think the game goes the way it did. He's been such a consistent big part of us that making saves like that is part of his game." -- Penguins forward Bryan Rust on goalie Matt Murray's save against Anthony Beauvillier in the third period
"It's tough to swallow, but the point is a point. Obviously we're going to take that point, but I think the upsetting part is we left one out there [that] we should have been able to get, and we didn't. We'll regroup here, and we've got another one Saturday that we've got to prepare for." -- Islanders defenseman Ryan Pulock
Video: Couturier, Rust, Tavares, and Wilson net OT winners.
Need to know
The Penguins were without defenseman Kris Letang, who sustained a lower-body injury during a 6-4 loss at the Boston Bruins on Monday. … Cizikas has four points (two goals, two assists) in his past two games. … The Islanders killed both Penguins power plays; their penalty kill is 24-for-25 over the past eight games.
Video: NYI@PIT: Cizikas stakes early lead with nice backhand
Penguins: Host the Chicago Blackhawks on Saturday (7 p.m. ET; NHLN, ATTSN-PT, NBCSCH, NHL.TV)
Islanders: Host the Florida Panthers on Saturday (Barclays Center; 1 p.m. ET; MSG+, FS-F, NHL.TV)
Video: Penguins rally in 3rd, end Isles' win streak in OT