The victory also put Tech in the ACC championship game Dec. 5 in Tampa, Fla.
Nesbitt passed for 195 yards with two scores and gained 110 rushing yards with one touchdown. Dwyer gained 110 yards on 14 carries with two touchdowns.
Demaryius Thomas scored once on two receptions for 89 yards. Orwin Smith's 83-yard kickoff return keyed the Yellow Jackets' rally from an early 10-0 deficit and led them to 49 unanswered and the ACC Coastal Division title with their 10-1 ( 7-1 ACC) record.
Duke's Thaddeus Lewis completed 22-of-35 passes for 212 yards with a touchdown and one interception.
Re'quan Boyette scored once on six catches for 65 yards for the Blue Devils (5-5, 3-3), who rushed for only 25 net yards in their second straight loss.