The Redskins 17-16 win over the New York Giants puts the team in a tie for second place with the Dallas Cowboys in the NFC East, but they need to maintain a balance on offense in order to make the playoffs. (Mike Jones and Jayne Orenstein/The Washington Post)

The Washington Redskins played a meaningful game in December on a big Monday night stage and were up to the moment, tightening the NFC East race and improving their playoff chances by beating the New York Giants, 17-16, at FedEx Field.

The Redskins extended their winning streak to three games — all against NFC East foes — and evened their record at 6-6. They moved back into a second-place tie with the Dallas Cowboys, just a game behind the division-leading Giants (7-5) with four games left. The Redskins also pulled to within a game of the Seattle Seahawks (7-5) in the chase for the second of two wild-card playoff spots in the NFC.

“We knew three weeks ago that every game we played was like a playoff game,” Redskins Coach Mike Shanahan said after the win.

It wasn’t the most spectacular of nights for Redskins rookie quarterback Robert Griffin III, who had thrown four touchdown passes in each of the team’s previous two wins. He passed for a relatively modest 163 yards.

But Griffin ran for 72, setting a single-season NFL record for rushing yards by a rookie quarterback. And he threw an eight-yard touchdown pass to wide receiver Pierre Garcon with 11 minutes 31 seconds remaining to put the Redskins in front. They held on from there.

The Redskins’ other touchdown came on a first-half fumble recovery by wide receiver Josh Morgan, who plucked a Griffin fumble from the air and ran the ball into the end zone.

“Sometimes you’ve got to get a little bit lucky,” Shanahan said.

Tailback Alfred Morris lost a costly second-half fumble but ran for 124 yards for the Redskins. He passed the 1,000-yard rushing mark and set a single-season team record for rushing yards by a rookie. The Redskins had 207 rushing yards. Garcon had a second consecutive highly productive game, with eight catches for 106 yards.

The Giants controlled the ball and, seemingly, the game for much of the evening. Quarterback Eli Manning threw for 280 yards and had a first-half touchdown pass to tight end Martellus Bennett. But that was the Giants’ lone touchdown to go with three field goals by place kicker Lawrence Tynes.

“It’s a great feeling,” Redskins defensive end Stephen Bowen said of the win. “In the second half, we dedicated ourselves and we said, ‘We’ve got to get it done. The season’s on the line.’ ”

Said defensive tackle Barry Cofield: “We tightened up a lot [on defense] in the second half. . . . We’re still not in control, but we feel like if we keep winning, we’re in a good spot.”

The Giants were coming off an impressive performance in a lopsided triumph at home over the Green Bay Packers eight days earlier. That win ended a two-game losing streak for the defending Super Bowl champions, and quieted the talk before the team’s bye week that Manning had been suffering from a tired arm.

But the Giants weren’t as sharp on offense in the early going Monday. They slowed their own drives with penalties. Tynes missed a 43-yard field goal in the second quarter, and Manning and his receivers failed to capitalize on a few occasions when they had chances for big plays. Even so, the Giants were churning out third-down conversions, and Tynes hit a 40-yard field goal as time expired in the first half to give them a 13-10 lead.

Tynes had given New York a first-quarter lead with a 39-yard field goal, but the Redskins had a swift reply with their fortunate-bounce touchdown on Griffin’s fumble. It came at the end of a 12-yard run by the Redskins’ quarterback, who had the ball swiped from his hand by Giants safety Stevie Brown just before Griffin hit the turf. But Morgan grabbed the ball ran 13 yards for a touchdown.

The Redskins’ good luck continued when Tynes pulled a field goal try wide left to end the Giants’ next possession early in the second quarter. But the Giants got the ball back and crafted an 85-yard touchdown drive, aided by a 30-yard completion from Manning to wide receiver Victor Cruz on a third-and-10 play. Manning found Bennett open in the middle of the end zone for a four-yard touchdown.

Griffin had completions of 18 and 35 yards to Garcon as the Redskins moved to the Giants 12-yard line. But their drive stalled, with Griffin throwing incomplete toward Garcon in the end zone on third down, and the Redskins had to settle for a 33-yard field goal by place kicker Kai Forbath. That tied the score at 10. But the Redskins left 41 seconds on the clock for Manning, who used a 28-yard completion to Bennett to set up Tynes’s 40-yard field goal to end the half.

The Redskins had a chance to reclaim the lead in the third quarter after a 46-yard dash by Griffin. But they squandered the opportunity when Morris lost a fumble at the Giants 9. A Manning-to-Cruz completion for 49 yards put the Giants in position for Tynes’s third field goal of the night, a 35-yarder that upped the lead to 16-10.