USC (7-6) became the first preseason No. 1 team to lose six games. It's also all but assured of becoming the school to enter the season on top of The Associated Press poll and finish unranked since Mississippi in 1964.
Washington's 1-yard touchdown run in the third made it 14-7, and he found Orwin Smith for a 17-yard touchdown pass in the fourth.
"I'm really proud of our football team," Georgia Tech coach Paul Johnson said. "I thought that they showed up and played with a lot of heart and a lot of determination, and I know Southern California has some really good football players. It was a hard-fought game."
Barkley, the first three-time captain in USC history, injured his right shoulder in a loss to UCLA and was not cleared to play his final college game. He clapped as the Trojans took the field for their first bowl game after a two-year NCAA ban.
Max Wittek tossed a 9-yard touchdown pass to Silas Redd in the second quarter, but also threw three interceptions. Redd added 88 yards rushing on 17 carries.
Talented receiver Robert Woods was limited to three receptions for 33 yards in what was likely his final college game. The junior said after the loss he plans to enter the NFL draft.
Kiffin said he took responsibility for the lost season.
"All of it," he said. "We can't be 7-6. That's not USC, and that's not our expectations. That's not why we came here. Obviously, we have some work here to get that fixed.
"Even if we'd won this game, we'd still be very disappointed in this season. It's well below our standards."
Asked if he thought the loss could cost him his job, Kiffin answered flatly, "No."
The Trojans struggled to contain Georgia Tech's triple-option attack. The Yellow Jackets (7-7) rushed for 294 yards on 63 carries while stopping a seven-bowl losing streak.
"I'm just glad we got the win," Washington said.
Georgia Tech 21, USC 7
Southern Cal 0 7 0 0 7
Georgia Tech 0 7 7 7 21
GaT • Sims 3 pass from Lee (Tanner kick), 10:41.
USC • Redd 9 pass from Wittek (Heidari kick), :50.
GaT • Washington 1 run (Tanner kick), 12:23.
GaT • O.Smith 17 pass from Washington (Tanner kick), 13:11.
Attendance • 47,922.
First downs 10 18
Rushes-yards 22-98 63-294
Passing 107 75
Comp-Att-Int 14-37-3 5-10-1
Return Yards 71 85
Punts-Avg. 8-44.0 7-40.4
Fumbles-Lost 1-0 2-2
Penalties-yards 2-10 8-88
Time of Possession 23:35 36:25
Rushing • Southern Cal, Redd 17-88, Wittek 1-5, McNeal 3-5, Lee 1-0.
Georgia Tech, Sims 17-99, Laskey 6-60, Lee 10-52, Washington 16-46,
Bostic 2-14, Godhigh 3-13, O.Smith 4-9, Zenon 2-7, Days 1-(minus 2),
Team 2-(minus 4).
Passing • Southern Cal, Wittek 14-37-3-107. Georgia Tech,
Washington 3-5-0-49, Lee 2-5-1-26.
Receiving • Southern Cal, Lee 6-41, R.Woods 3-33, Redd 3-14,
Grimble 2-19. Georgia Tech, Je.Moore 1-27, C.Jackson 1-23, O.Smith 1-17, Bostic 1-5, Sims 1-3.