Former Peterborough midfielder Potter came off the bench to fire an 88th-minute winner for the hosts at the Kassam Stadium.
It was Oxford's fourth successive victory over their derby rivals as Swindon boss Paolo Di Canio was again left to rue the failings of his misfiring League One side.
Beaten 4-1 by Preston on Sunday, Swindon were much the better side in an entertaining contest but squandered a hatful of chances and were punished for it.
New signing Giles Coke, Raffaele De Vita, Darren Ward and Adam Rooney all had good opportunities before the hosts broke with two minutes remaining and Potter struck.
Potter's second goal of the season was clinical as he latched on to James Constable's left-wing cross, although the winner could have been avoided with defenders Ward and Aden Flint to blame after colliding in their own box.