ATLANTA -- From Washington's first possession to the decisive play in the final minute, Atlanta's defense kept finding ways to get its hands on the ball.
One of five rookies to start for the defense made the biggest play of the game.
"You can't win with turnovers, yet we still had an opportunity to win and that shows you how hard they fought," said Redskins coach Mike Shanahan.
"Those guys normally are great with ball security and don't turn it over."
Cousins passed for 381 yards and three touchdowns, but had three turnovers in his first start of the season after Shanahan benched Robert Griffin III. Griffin was not in uniform and watched from the sideline.
Cousins' 3-yard touchdown pass to Moss gave Washington a chance to force overtime by kicking the extra point.
Instead, Cousins' 2-point pass for Pierre Garcon was deflected by Trufant, who also had an interception.
"I was telling myself I had to make some big plays," Trufant said. "I wasn't surprised they went for the win. They had the confidence and we were up for the challenge."
Shanahan said his decision to go for 2 was based on the Falcons' defensive alignment. He said he would have used his final timeout to send his kicking team on the field if the Falcons didn't have the alignment he wanted for his planned play.
"I thought if we had the right defense and the right play, we're going to stay with it," Shanahan said. "We thought we did and unfortunately it didn't work out."
Shanahan brushed off a question about his job status, saying "I'm not going to talk about that."
Cousins said he liked the decision to go for 2.
"I loved the call to go for 2 there," Cousins said. "I felt like we had them on the ropes. We just didn't do enough to execute, but it starts right here with me."
The Falcons recovered an onside kick to seal the win.
"It was a game full of drama, but I'm glad we were able to pull it off," said Atlanta's Steven Jackson, who ran for 38 yards and two touchdowns.
Cousins listed his two interceptions, lost fumble and failed 2-point pass as "four plays right there that if they go differently, it's probably a much better result."
The Falcons started five rookies on defense, including three in the secondary.
Rookie offensive tackle Ryan Schraeder also made his first start for Atlanta.
Morris had 98 yards rushing on 18 carries, including a 37-yard run.
Cousins lost a fumble on the Redskins' first possession and set up the Falcons' go-ahead touchdown late in the third quarter with his first of two interceptions.
The Falcons led 24-20 with less than 6 minutes remaining before Trufant's interception set up Matt Bryant's 51-yard field goal.
The teams combined for six turnovers in the first half, including four turnovers by the Redskins. There were lost fumbles on three straight plays in the second quarter.
The Redskins had an excellent scoring opportunity at the Atlanta 18 following a 62-yard pass from Cousins to Aldrick Robinson.
On first down from the 18, Morris lost the ball without being hit, and Malliciah Goodman recovered for Atlanta.
The Falcons gave the ball back when Matt Ryan fumbled when hit by Ryan Kerrigan. On the next play, Cousins passed to Moss, who lost the ball when stripped by Robert McClain. William Moore recovered for Atlanta.
Ryan completed 29 of 38 passes for 210 yards with one touchdown and one interception.
Falcons tight end Tony Gonzalez had six catches for 62 yards and a touchdown. He became the fifth player in NFL history with 15,000 yards receiving.
The Redskins also lost five fumbles against the Oilers on Oct. 30, 1988. ... Garcon had seven catches for 129 yards, including a 53-yard touchdown. ... Falcons DT Jonathan Babineaux recovered two fumbles. ... Signs spotted in the stands held by Redskins fans: "Free RG III," "Let 'em play" and "We still believe in RG III." ... Falcons LB Sean Weatherspoon left the game with a knee injury.
Tom Brady has won his appeal against the NFL, with U.S. District Judge Richard M. Berman criticizing commissioner Roger Goodell for dispensing "his own brand of industrial justice."
Tom Brady wasn't even present for Thursday night's preseason finale between the Patriots and Giants at Gillette Stadium, but he was still the story of the night.
In his weekly radio interview, Patriots president Jonathan Kraft said the team feels vindicated by a federal court decision to overturn Tom Brady's ban and that the team is "ecstatic" for Brady.
Tim Tebow threw two touchdown passes against his former team in a strong effort to make his new team's 53-man roster.
Jason Pierre Paul plans to return to the New York Giants next week and the team will examine his hand and make a determination about when he might be available to play, according to a source.
The decision to vacate Tom Brady's suspension could impact how many games Greg Hardy plays for the Cowboys in 2015, as he will confer with the NLFPA whether to challenge his own ban in court.