Washington also threw for 185 yards as Georgia Tech (8-3, 5-3 ACC) amassed 364 rushing yards on the day.
David Sims found the end zone twice, with his second giving the Yellow Jackets a 21-7 lead early in the second quarter.
Embry Peeples contributed 64 yards and one touchdown in Georgia Tech's win.
Sean Renfree had a big day for Duke (3-8, 1-6), but it wasn't enough. He compiled 250 aerial yards and four touchdowns in the Blue Devils' loss.