Then Alford ended the game.
The Redskins had the first possession of OT and Cousins moved the team to midfield. On second and 8 from the 50, Ryan Grant slipped while trying to adjust to Cousins' pass. Alford was in perfect position for the interception before racing down the sideline for the touchdown.
"I trusted my instincts and the film study," Alford said. "... I just jumped it, and it was there for me to make a play on. I looked back to see who was around me, and once there was nobody around me, it was off to the end zone."
Near the end of his sprint toward the goal line, Alford held the ball high with both hands and did a high-step, Deion Sanders style.
Atlanta's other starting cornerback, Desmond Trufant, wears the No. 21 Sanders made famous in Atlanta, but the Prime Time play of the day belonged to Alford.
Cousins said he felt pressure from Atlanta's pass rush before trying to complete the pass to Grant.
"I was hot off the left side and felt need to get rid of the football and not take a sack and kill the drive," Cousins said. "... I made the throw and the guy made the play and that was it."
Alford had a pass interference penalty in the fourth quarter to set up a Washington touchdown.
Grant was not available for postgame interviews.
Atlanta trailed 16-12 before Devonta Freeman's 6-yard scoring run with 24 seconds remaining in regulation. The Falcons (5-0) are the first team to start 5-0 when trailing in the fourth quarter of four games.
Freeman had an apparent 13-yard scoring catch ruled incomplete on a review two plays before his scoring run.
Freeman had 27 carries for 153 yards and the touchdown. He is the first NFL player with seven rushing touchdowns in his first three starts.
Dustin Hopkins' 52-yard field goal for Washington on the final play of regulation forced overtime.
The Falcons overcame two interceptions and a lost fumble by Matt Ryan, who completed 24 of 42 passes for 254 yards with no touchdowns.
The Redskins (2-3) were denied their first back-to-back wins in almost a year -- since Weeks 7 and 8 in 2014.
"This is a tough one, man," said Redskins coach Jay Gruden. "We had an opportunity. ... Our receiver slips and falls and they get a pick six. Ryan Grant just slipped and fell. It's unfortunate."
The interception was the second of the game for Cousins, who completed 21 of 32 passes for 219 yards with one touchdown.
Matt Jones' 1-yard run midway through the final quarter gave Washington a 13-12 lead.
Julio Jones, who began the day leading the NFL in catches, and Roddy White were held without a catch in the first half. Jones finished with five catches for 67 yards. White, who complained about his diminished role early in the week before meeting with coach Dan Quinn, had two catches for 23 yards.
White's first catch of the day, a 16-yarder, moved the Falcons to the Washington 14 in the fourth quarter. Freeman ran for 11 yards and Atlanta again gave the ball to Freeman. He was stripped by defensive end Chris Baker near the 2 and the ball bounced into the end zone. Jones fell on the fumble for a touchdown.
Ryan's pass for Leonard Hankerson on the 2-point attempt was incomplete.
Washington had a quick answer. Following a pass interference call against Alford, Jones' 1-yard run gave Washington a 13-12 lead; Cousins' pass for Pierre Garcon was incomplete on the 2-point attempt.
Cousins' first-quarter 7-yard pass to tight end Derek Carrier was the only touchdown for either team through three quarters. The Falcons tried to keep pace with field goals, but twice the uprights got in the way of the usually reliable Matt Bryant's attempts.
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