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The reigning Super Bowl champions were coming off a bye week looking to atone for their defeat against the New Orleans Saints.
But they were stunned by a team without a win in the last month on a difficult afternoon for seven-time Super Bowl winner Brady - the Bucs dropping to a 6-3 record.
Brady threw two second-half touchdowns, but Washington (3-6) produced an impressive fourth-quarter drive that ended with Antonio Gibson's second rushing score putting the result to bed.
"Not a great day of football for us," Brady, who finished 23-of-34 for 220 yards, said.
"We just never really played on our terms. We played from behind the whole game, and they played a good game."
Brady's former team the New England Patriots extended their winning run to four games with a stunning 45-7 thrashing of the Cleveland Browns.
The Buffalo Bills (6-3) responded to their embarrassing loss to the Jacksonville Jaguars last week by swatting aside the New York Jets 45-17.
The Dallas Cowboys were another team to comprehensively bounce back from a defeat as they hammered the Atlanta Falcons 43-3.
Dak Prescott threw two touchdowns to CeeDee Lamb and rushed in for another while running back Ezekiel Elliott also crossed the goal-line twice, ending any concerns the Cowboys (7-2) had been figured out in their comprehensive loss to the Denver Broncos last Sunday.
The Detroit Lions' winless run to start the season continued with a 16-16 tie after overtime with the Pittsburgh Steelers.
The Tennessee Titans (8-2) still have the best record in the AFC thanks to a battling 23-21 triumph over the New Orleans Saints.
The Green Bay Packers also moved to 8-2 with Aaron Rogers returning to conduct a 17-0 shutout at home over the Seattle Seahawks.
NFC rivals Arizona dropped just their second game of the season, the Cardinals going down 34-10 to the Carolina Panthers who welcomed back star quarterback Cam Newton.
The 2015 NFL MVP who was re-signed earlier this week made his presence felt on his first play of the game.
The 32-year-old found the end zone for a two-yard touchdown before ripping off his helmet, which drew an unsportsmanlike penalty, and screamed "I'm back!" as his teammates celebrated around him.
"I'm just floating at an all-time high frequency," Newton said.
"It's almost scary."
Elsewhere, the Kansas City Chiefs defeated the Las Vegas Raiders 41-14, with Patrick Mahomes throwing for 406 yards and five touchdown passes.
The Indianapolis Colts scored a 23-17 victory over the Jacksonville Jaguars, the Philadelphia Eagles were 30-13 winners at the Denver Broncos, and the Minnesota Vikings beat the Los Angeles Chargers 27-20.