Trailing 3-0 after Lawrence Tynes' 39-yard field goal on reigning Super Bowl champion New York's opening possession, the Redskins went ahead by going 80 yards on only four plays—including a wacky one for the score.
On second-and-2 from New York's 28, Heisman Trophy winner Griffin ran to his left and was being tackled by safety Stevie Brown after what would have been a 12-yard gain.
But as the dynamic rookie quarterback fell with his back to the ground, the football popped out, and went right to Morgan 3 yards farther upfield.
Morgan broke through two would-be tacklers at the goal line for the TD with a little under 4 1/2 minutes left in the first quarter. After being reviewed, the original call of a score stood.
It's the second time this season a fumble by the man known as RG3 was picked up and taken into the end zone by a Redskins receiver. Pierre Garcon did it in a victory over Tampa Bay on Sept. 30.
Monday's first quarter also included a 19-yard gain by Redskins running back Alfred Morris, making him only the second Washington rookie to top 1,000 yards rushing. Reggie Brooks did it 1993.
New York had gone ahead with an 11-play, 69-yard possession that lasted 6
The Giants entered the game in first place in the division with a 7-4 record and coming off a turnaround 38-10 victory over the Green Bay Packers.
The Redskins came in 5-6, but with a two-game winning streak that made them believe their once-disastrous season could eventually result in a playoff berth.
The first meeting between the Redskins and Giants, at the Meadowlands in Week 7 in October, ended with a 27-23 victory for New York, thanks to Manning's 77-yard touchdown pass to Victor Cruz with 73 seconds left.
Redskins linebacker London Fletcher and left tackle Trent Williams, who were limited in practice by injuries Friday and Saturday, both started Monday night. The 37-year-old Fletcher extended his consecutive games streak to 236—every game in his 15-year NFL career.
Giants receiver Domenik Hixon was inactive, but safety Kenny Phillips (right knee), defensive end Jason Pierre-Paul (back) and offensive tackle David Diehl (shoulder) were available.
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