Julio Jones had 10 receptions for 94 yards, including an 18-yard catch with both feet barely inbounds that gave Atlanta the lead early in the fourth quarter.
Griffin was injured early in the second half while trying to scramble for the end zone on third-and-goal from the 3. As he went down, he took a solid hit to the helmet from the upper body of linebacker Sean Weatherspoon. Clearly rattled, the No. 2 overall draft pick had his head examined on the sideline before being taken to the locker room.
Coach Mike Shanahan said Griffin suffered a "mild concussion." Team spokesman Tony Wyllie said the quarterback was examined by an independent neurologist before being sent home from the stadium and will be evaluated again Monday.
Griffin's susceptibility to injury was a concern when he was hammered hard while carrying the ball frequently in the option in the Redskins' first three games, but Shanahan went with a more conventional approach in the last two games. Griffin did not have a designed run on Sunday, yet he nevertheless had to leave a game for the first time in his young career.
Griffin was 10 for 15 for 91 yards when he was hurt. The play after his injury, Billy Cundiff converted a 23-yard field goal that gave the Redskins (2-3) a 10-7 lead.
Kirk Cousins, a fourth-round pick from Michigan State making his NFL debut, entered in place of Griffin and went three-and-out in his first possession. The Falcons then took advantage of Sav Rocca's shanked punt to drive 47 yards for a touchdown on Jones' catch.
But Cousins gave the Redskins the lead again about a minute later, when Santana Moss ran deep down the middle without a defender anywhere near him. The 77-yard pass made the score 17-14 early in the fourth quarter.
Ryan then cobbled two scoring drives that gave the Falcons the win. Matt Bryant's 53-yard field goal with 7:42 remaining tied the score, and a 29-yard pass to Jones was the key play in a 69-yard drive that led to Turner's decisive touchdown.
Cousins had two more chances to rally the Redskins, but he was intercepted twice in the final two minutes. He finished 5 for 9 for 111 yards.
Alfred Morris ran for 115 yards on 18 carries for Washington.
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Atlanta 24, Washington 17
Atlanta 0 7 0 17 24
Washington 0 7 3 7 17
Was • Kerrigan 28 interception return (Cundiff kick), 10:11.
Atl • Gonzalez 1 pass from Ryan (Bryant kick), :30.
Was • FG Cundiff 23, 5:56.
Atl • Jones 18 pass from Ryan (Bryant kick), 13:23.
Was • Moss 77 pass from Cousins (Cundiff kick), 12:24.
Atl • FG Bryant 53, 7:42.
Atl • Turner 13 run (Bryant kick), 2:46.
Attendance • 75,337.
First downs 28 12
Total Net Yards 421 316
Rushes-yards 28-83 21-129
Passing 338 187
Punt Returns 2-2 3-22
Kickoff Returns 2-36 4-113
Interceptions Ret. 2-28 1-28
Comp-Att-Int 34-52-1 15-24-2
Sacked-Yards Lost 1-7 3-15
Punts 6-48.8 6-42.3
Fumbles-Lost 1-1 0-0
Penalties-yards 2-13 4-20
Time of Possession 37:01 22:59
Rushing • Atlanta, Turner 18-67, Douglas 1-5, Ryan 4-4, Rodgers 3-4, Snelling 1-2, Jones 1-1. Washington, Morris 18-115, Griffin III 1-7, Grant 1-5, Hankerson 1-2.
Passing • Atlanta, Ryan 34-52-1-345. Washington, Cousins 5-9-2-111, Griffin III 10-15-0-91.
Receiving • Atlanta, Gonzalez 13-123, Jones 10-94, White 4-68, Douglas 2-34, Turner 2-2, Snelling 1-9, Rodgers 1-8, Gallarda 1-7. Washington, F.Davis 5-54, Garcon 3-24, Moss 2-80, Morris 1-20, A.Robinson 1-10, Royster 1-7, Morgan 1-4, Hankerson 1-3.
Missed Field Goals • Washington, Cundiff 31 (WR).