WASHINGTON -- New York Islanders goalie Christopher Gibson admitted he was nervous facing the Washington Capitals in his first NHL start.

He hid it well.

Gibson made 29 saves, Thomas Hickey scored with 2:47 left in overtime and the Islanders clinched a playoff berth with a 4-3 win over the Capitals on Tuesday night.

New York (43-26-9) rallied from a 3-1 deficit in the third period to force overtime and Gibson stopped Evgeny Kuznetsov on a breakaway 30 seconds into the overtime.

"In my mind I was like, 'I have to stop this to keep this going,'" Gibson said. "Lucky enough I made the save there, and we won the game."

Hickey, who left the ice earlier in the overtime after taking a skate to the chin, returned and ended things when he scored off a feed from John Tavares on a rebound.

"It happened so quick," Hickey said of the game winner. "All of a sudden you just go to the net and there it is. It just pops out and the next thing you know you're in here."

Tavares scored his 31st goal of the season and added two assists for the Islanders. Kyle Okposo and Anders Lee also scored for New York, which secured at least a wild-card berth with the win.

"Since day one of training camp they had a goal," Islanders head coach Jack Capuano said. "You want to get to the dance to give yourself a chance to win a Stanley Cup and they've done that."

Alex Ovechkin scored twice for Washington (55-18-6), which has lost three of its last four games. T.J. Oshie added a goal and two assists.

Braden Holtby made 23 saves. He has 47 wins - one behind the NHL record of 48 set by New Jersey's Martin Brodeur in 2006-07 – and the Capitals have three games left, including back-to-backs to end the regular season.

"He's been our MVP," Washington head coach Barry Trotz said regarding the team's motivation to help Holtby get the record. "I'll just put it out there. He's been our best player probably all year. The guys recognize that and they would like to be a part of the record."

With two goalies injured and Thomas Griess having played Monday night, the Islanders recalled Gibson from AHL Bridgeport to make the start.

"At the beginning I was a little nervous, but once I got going, I was fine," Gibson said.

Capuano said: "He gave us a chance to win the game and [he was] our best player tonight."

Oshie and Ovechkin gave the Capitals a 3-1 lead when they scored in the opening seven minutes of the third period. Ovechkin's goal came at the conclusion of pretty passing sequence involving Oshie and Marcus Johansson (two assists).

The Islanders pulled within 3-2 when a puck deflected off the boards behind Holtby and out in front to Okposo, who banged it home at 8:40 of the period for his 22nd goal of the season.

"I just missed it somehow," Holtby said of his inability to stop the puck when it came off the boards. "I got caught between covering it and putting it in the corner, and when you're in between decisions, it never ends up well…It's unfortunate because it was a turning point in the game."

Just 1:45 later, the score was 3-3 after Lee deflected a Nick Leddy shot past Holtby.

The already banged-up Islanders were without D Brian Strait (upper body injury) for the final 20 minutes.

Ovechkin, who has 13 goals in his last 12 games against New York, opened the scoring at 4:29 of the first period when he and fired a high wrist shot from a tough angle past Gibson.

Tavares hit the crossbar in the opening minute of the second period but found the back of the net before the next intermission. He one-timed a drop pass from Hickey past Holtby on the glove side at 13:33 of the period.

NOTES: The Capitals took the season series 3-1. … Washington C Nicklas Backstrom (upper body injury) missed his third straight game. D Mike Weber, D Taylor Chorney and RW Stanislav Galiev were scratched. ... Islanders G Christopher Gibson's only other NHL action came Jan. 2 when he played 29 minutes against the Penguins. ... The Islanders scratched G Jean-Francois Berube (lower body), C Mikhail Grabovski (upper body), G Jaroslav Halak (lower body), RW Cal Clutterbuck (undisclosed), D Calvin De Haan (undisclosed) and RW Travis Hamonic (knee). D Marek Zidlicky and C Shane Prince also were scratched.