Pulling off the improbable, the Washington Redskins went up to MetLife Stadium and overcame an ugly start against the NFC East-leading New York Giants to come away with a 23-10 victory Sunday afternoon.

It was the Redskins’ fifth win and, in beating the Giants for a second time this season, Washington registered the first sweep of its division rival since 1999.

“The Giants, they’ve really been our nemesis around here the last five years,” said Redskins linebacker London Fletcher, whose team had fallen to New York nine of the last 10 games entering this season. “To sweep them, it means a lot, because they’re a well-coached football team.”

With quarterback Rex Grossman turning in a shaky performance, the Redskins relied heavily on their defense. Washington intercepted Giants quarterback Eli Manning three times, winning the turnover battle for the first time all season.

And when Manning went to work in the final quarter — aiming for his seventh fourth-quarter comeback victory of the season — the Redskins twice denied the Giants in the shadow of their own end zone.

Manning finished the game 23 for 40 for 257 yards and no touchdowns. Ahmad Bradshaw led New York in rushing with 10 carries for 58 yards and a touchdown.

Grossman connected on 15 of 24 passes for 185 yards and a touchdown but threw two interceptions. Roy Helu’s streak of three 100-yard rushing games came to an end as the rookie picked up 53 yards on 23 carries while Evan Royster added 36 yards on 10 carries. Jabar Gaffney led Washington with six catches for 85 yards.

“You feel good about the way they played,” Coach Mike Shanahan said of his team, which had lost two straight and last week fell short in a last-second bid to upset the New England Patriots. “I was really disappointed that we couldn’t close the door last week. . . . So to finish the way we did today was nice.”

Washington’s first defining goal-line stand came three minutes into the fourth quarter. After the Redskins extended their lead to 23-3 with 14 minutes 57 seconds left, the Giants finally started showing signs of life. Manning completed four straight passes to march his team to the Redskins 13-yard line.

But on his fifth pass attempt, Manning’s fortunes changed. Redskins cornerback Josh Wilson made a leaping catch in the end zone for an interception and touchback. It was Wilson’s second interception of the season, and his second straight game with a pick.

The Redskins’ defense answered the bell again later in the fourth quarter. Wilson made a strong tackle to deny Giants running back D.J. Ware as he caught a pass and tried to cross the goal line. Initially, the officials ruled the play a touchdown. But a review showed that Ware had bobbled the ball at the line and didn’t secure possession until Wilson wrestled him back the 2.

With the Giants facing fourth and goal from there, Redskins linebacker Brian Orakpo rushed from the edge and drew a holding call from tackle David Diehl, backing the Giants up to the 12-yard line. New York tried for a touchdown on the next play, but rookie linebacker Ryan Kerrigan sacked Manning to deny the Giants and register Washington’s first sack of the game.

The Redskins were up 23-3 with just 4:03 left and a majority of the seats in the stadium empty before New York finally moved downfield to score on a three-yard touchdown by Bradshaw.

Washington got off to a forgettable start as Grossman threw an interception to cornerback Corey Webster on the first play of the game.

On the play — a called flea-flicker — Santana Moss had a three-step cushion on Webster, but Grossman held on to the ball too long and underthrew the pass. Webster turned, waited for the ball and caught a pass that traveled 49 yards. An unnecessary roughness call on Giants defensive tackle Chris Canty away from the ball backed the Giants up to the New York 18.

Washington held the Giants to three-and-out, then put together a 10-play, 52-yard drive that was capped by a 36-yard Graham Gano field goal.

On Washington’s next possession, Grossman threw another interception. Going deep for Gaffney on first and 10 from the Washington 20, Grossman overthrew the receiver and Kenny Phillips made the catch, giving New York the ball at its 27-yard line.

But Grossman redeemed himself on the following possession, and Washington’s offense started to click, fueled by crucial gains on third down. On the first play of the second quarter, on third and one, fullback Darrel Young picked up three yards to extend the drive.

Three plays later, on third and eight from the New York 20-yard line, Grossman found a wide-open Moss in the left corner of the end zone for a touchdown. It was Moss’s fourth touchdown catch of the season and Grossman’s 13th touchdown pass.

“When things go bad early, you usually have 55 minutes to fix that problem,” said Grossman, who completed 11 of 17 passes for 151 yards on that drive and thereafter. “You obviously don’t want to have that. But if you have something bad happen late in the game, you lose the game.”

The Redskins’ defense continued to hold the Giants in check and forced Steve Weatherford to punt a third time. Washington’s offense kept rolling, however, cranking out a nine-play, 41-yard drive capped by a six-yard touchdown run by Young — the first of his career.

New York got on the board in the final seconds of the half, going 46 yards in six plays. The Giants scored on a 40-yard field goal from Lawrence Tynes with seven seconds remaining.

A week after hurting his team by giving up on a play that led to a 49-yard gain by Patriots tight end Rob Gronkowski and being called for unsportsmanlike conduct for throwing an official’s flag, cornerback DeAngelo Hall provided a big play for the Redskins to start the second half.

Hall intercepted Manning with a one-handed grab and returned the ball 26 yards to the New York 34-yard line just two plays into the third quarter. The offense couldn’t fully capitalize, but Gano hit a 43-yard field goal to extend the lead to 20-3.

“We didn’t really lose hope,” Moss said. “Right now, we’re just playing and having fun. This is something that we should’ve been doing a long time ago. We’re going out there, our minds not really on nothing, no negative plays, no negative thoughts.”

More on Redskins vs. Giants

Mike Shanahan: ‘I know we will win’

Thomas Boswell: Gunslinging Grossman has his day

Jason Reid: DeAngelo Hall on top of his game, for now