LANDOVER, Md. — Robert Griffin III went down, the ball popped out, and the Washington Redskins scored a touchdown.

Look out, New York Giants and the rest of the NFC East. If the rookie quarterback keeps getting those kinds of breaks, it’ll be hard to keep him out of the title hunt for years to come.

As it is, RG3 has the Redskins within a game of first place, leading a fourth-quarter rally in a 17-16 Monday night victory over the Giants, giving Washington a three-game winning streak in which it has dispatched division rivals — Philadelphia, Dallas and now New York — one by one.

“We know that our backs are against the wall,” Griffin said. “And even though we won tonight, our backs are still against the wall.”

The Redskins (6-6) appeared out of the running at 3-6 a month ago, but Griffin is proving his team can never be counted out when he’s on the field.

With the Giants (7-5) losing three of four and the Cowboys (6-6) also at .500, the division is up for grabs.

Griffin did get another of his goals accomplished Monday by assuring Washington will win more games than last season’s 5-11 team.

“You can put a check by that one, but there’s a lot more goals that this team is stretching for and striving for,” Griffin said.

Griffin completed 13 of 21 passes for 163 yards and ran five times for 72 yards, breaking Cam Newton’s NFL record for yards rushing by a rookie quarterback.

His top target again was Pierre Garcon, who had eight receptions for 106 yards and a touchdown, showing no signs of the painful toe injury that forced him to miss six of the season’s first nine games.

Alfred Morris ran for 124 yards on 22 carries, becoming the second Redskins rookie to run for 1,000 yards. Reggie Brooks had 1,063 in 1993.

Washington also ended a 10-game home losing streak in Monday night games, with Griffin again showing his knack for winning on a big stage.

Eli Manning completed 20 of 33 passes for 280 yards and a touchdown for the Giants, who had won 26 in a row on the road when holding a halftime lead.

They were ahead 13-10 at the break Monday against the Redskins, but they failed to finish the job for the first time since blowing a 21-0 halftime lead in a 24-21 loss to Tennessee in 2006.

Ahmad Bradshaw ran for 103 yards on 24 carries, and Victor Cruz had five catches for 104 yards for the Giants, who were uncharacteristically penalty-prone, getting flagged nine times for 73 yards.

The Giants moved the ball well all game, but the drives produced three field goals by Lawrence Tynes and only one touchdown — Manning’s 4-yard pass to Martellus Bennett late in the first half.

The game’s final score was Griffin’s 8-yard pass to Garcon early in the fourth quarter, but the Redskins’ first touchdown was one of the evening’s crazy moments.

On second-and-2 from the New York 28, Griffin ran to his left and was being tackled by Stevie Brown after what would have been a 12-yard gain.

But as Griffin fell with his back to the ground, the ball popped out and went right on the fly to Washington receiver Joshua Morgan 3 yards farther upfield. Morgan then ran 13 yards for the score.

“We didn’t run (that play) in practice because we wanted to save it for the game,” Griffin said with a grin. “I knew he was going to be there for it. ... Joshua did a good job being in the spot where he was supposed to be.”

It was the second time this season that a Griffin fumble has turned into Redskins touchdown. Garcon recovered one in the end zone in a win over Tampa Bay.

Another fumble by the Redskins — this one by Morris in the third quarter — was recovered by the Giants and set off mayhem. New York defensive tackle Linval Joseph yanked at Redskins center Will Montgomery’s leg. Montgomery kicked at Joseph in response, and Joseph stomped at Montgomery. Joseph and a Redskins player were whistled for offsetting unnecessary roughness penalties.

Giants safety Tyler Sash left in the first half with a hamstring injury and eventually was ruled out for the game, and New York right tackle Sean Locklear was carted off with an injury in the fourth quarter.  

Redskins linebacker London Fletcher and left tackle Trent Williams, who were limited in practice by injuries Friday and Saturday, both started. The 37-year-old Fletcher extended his consecutive games streak to 236 — every game in his 15-year NFL career.