RALEIGH, N.C. — The New York Islanders don’t have John Tavares anymore. They still have playmakers.

Reigning rookie of the year Mathew Barzal set up Josh Bailey’s power-play winner 43 seconds into overtime, and the Islanders began their post-Tavares era by beating the Carolina Hurricanes 2-1 on Thursday night.

“That whole power play has been really good through the preseason,” Trotz said. “(Bailey) understands the spots. Obviously, it runs through Mathew on that one side. They’ve got a real good understanding.”

Valtteri Filppula also scored as the Islanders gave Trotz a victory in his debut with the team and spoiled Rod Brind’Amour’s first game behind the Carolina bench.

“The amount of work this whole staff has put in has been pretty remarkable, and the amount of information coming our way is overwhelming at times,” alternate captain Cal Clutterbuck said. “Good to see him get that first one. He’s a seasoned guy and I think he’s prepared us well.”

Trotz took over shortly after leading Washington to its first Stanley Cup, taking over after Doug Weight was fired. Brind’Amour, the captain of Carolina’s Cup-winning team in 2006, replaced Bill Peters after he left for Calgary. Tavares signed with Toronto as a free agent.

Jordan Staal sent it to OT by scoring a deflected goal with 1:35 remaining in regulation for Carolina, but the Islanders started overtime with a 4-on-3 advantage after Micheal Ferland was called for tripping Barzal with 3.2 seconds left.

Barzal threaded a cross-ice pass from the circle to Bailey, who ended it by snapping the puck past Mrazek.

“They made a great shot. They made a great play,” Carolina captain Justin Williams said. “Our goalie was there, but it was the perfect shot.”

Mrazek stopped 18 shots for Carolina. Thomas Greiss made 45 saves for the Islanders, and for a long while appeared headed for another save-heavy shutout in Raleigh. He also stopped 45 shots in a 3-0 victory over Carolina on Feb. 16.

“They like to shoot the puck, that’s what it is,” Greiss said.

But with Mrazek on the bench for an extra attacker, Dougie Hamilton uncorked a blast that clipped Staal’s backside on its way past Greiss. The goal stood following a review to determine whether Ferland interfered with the Islanders goalie.

“We dug in,” Brind’Amour said. “We didn’t just fold.”

Both teams enter the season optimistic that their meager recent playoff histories are just that — history.

The Islanders, who have just one playoff series win since 1993, have made the postseason just three times in the past 11 years.

The Hurricanes have been worse. They’ve made the playoffs just once since Brind’Amour hoisted the Cup, and their nine-year postseason drought is not only the longest active dry spell in the league but one year shy of matching the NHL record for futility.

A bad omen for them, perhaps: Since the lockout that wiped out the 2004-05 season, the Hurricanes have not made the playoffs in any season in which they lost their first game at PNC Arena.

“We’re planning on playing a lot more than 82 games this year,” Williams said. “This was just one. One that didn’t go our way.”

Six players — led by No. 2 overall draft pick Andrei Svechnikov — made their debuts with the new-look Hurricanes, including Mrazek, who signed with Carolina in July after club stalwart Cam Ward left for Chicago. He drew the start on opening night after Scott Darling injured his hamstring in the preseason finale four days earlier against Nashville.