Tailback Jonathan Dwyer also ran for two scores for the Yellow Jackets (5-1, 3-1 Atlantic Coast Conference), who won for the first time in Tallahassee where the Seminoles have now lost five straight to Football Bowl Subdivision opponents.
Florida State players came onto the field before the kickoff arm-in-arm in a show of unity with their embattled 79-year-old coach in the middle of the front row.
Bowden has been in the middle of a weeklong controversy about his coaching future after the chairman of the university's board of trustees said earlier this week that the 79-year-old coach should retire at the end of the season.
A threatened blackout by protesters who favor Bowden's departure failed to materialize in any noticeable way and the coach was loudly applauded when his name was first voiced on the stadium public address system.
Florida State (2-4, 0-3 ACC) wasted another spectacular performance by junior quarterback Christian Ponder, who completed 26 of 38 passes for a career best 359 yards and five touchdowns.
But it wasn't enough to keep Florida State from its poorest start since Bowden's first season here in 1976.
Nesbitt, who ran for a game-high 140 yards, also threw a 73-yard touchdown pass to Demaryius Thomas in the third quarter that tied the game at 35.
Diminutive Marcus Wright's 19-yard touchdown run put the Yellow Jackets ahead for good at 42-38 late in the third quarter and Nesbitt iced the outcome with a 22-yard scoring run with 6:29 left in the game.
Georgia Tech's defense settled down in the second half after being embarrassed early.
At halftime, Florida State had piled up 403 yards offense and 21 first downs behind a near-perfect Ponder, who completed 18 of 21 passes for 267 yards and four touchdowns as the Seminoles led 35-28 at the break.
Officials stopped play for 78 minutes because of lightning with 6:50 left in the first quarter and the teams tied 7-7. The quarter ended at 9:59 p.m. with the score tied at 14 and the teams already combining for 308 yards of offense.