Despite being a league apart the Magpies put on a tremendous second half performance to put Swindon on the back foot and earn themselves a deserved replay.
It didn't start well for the visitors as Swindon poured forward with Rory Fallon heading wide a Steve Robinson cross on 14 minutes before five minutes later they took the lead.
Sammy Igoe's corner found captain Sean O'Hanlon six yards out and he made no mistake with a bullet header past keeper Saul Deeney.
But despite taking the lead Swindon failed to capitalize on their advantage and it was County who went close twice before half-time.
Midfielder Oakes warmed Swindon keeper Rhys Evans' gloves with a 30-yard free-kick on 26 minutes before the former England under-21 goalkeeper produced a world-class save ten minutes before the break.
Matthew Gill's long throw caught out the Swindon defence and defender Kelvin Wilson waltzed through only to see his side-footed effort from six yards somehow pushed round the post by Evans.
Swindon midfielder Brian Howard tested keeper Deeney with a 25-yard left-foot shot on the hour before Notts County midfielder Chris Palmer took centre stage.
The tricky winger caused havoc on the left wing and almost forced an equaliser on 64 minutes when his cross from the left fizzed past the far post with David Pipe inches away from a tap in.
Palmer then hit two shots wide as County poured forward before they were rewarded deep into injury time.
Substitute Tony Scully swung in a corner from the right and Oakes found himself unmarked at the far post to chest down and hit a sweet half volley past keeper Evans.