King gained 166 yards on 18 carries and his touchdowns led Georgia to a 24-10 lead with 13:08 left in the third quarter.
Washaun Ealey led Georgia's running game with 183 yards on 20 carries, and Blair Walsh kicked three field goals for the Bulldogs (7-5), who scored 10 points after two Tech turnovers.
Nesbitt led Tech with 177 offensive yards -- 136 passing and 41 rushing -- with a touchdown pass and a TD on the ground.
Thomas caught five passes for 128 yards, but Jonathan Dwyer was held to 32 yards on 14 carries with one touchdown for the Yellow Jackets (10-2), who have lost eight of their last nine meetings with Georgia.
Celebrity Breakups and divorces of 2014 [PHOTOS]