But the FA Cup replay lacked the quality or excitement of the first tie at Whaddon Road, which was possibly not surprising as it was the third meeting between the two sides in the last 10 days.
Cheltenham deserved to go through, but Oxford protested angrily that the free-kick from which Wilson hit the winner should never have been given.
Referee Andy Penn penalised Chris Willmott, but it looked to many as though Kayode Odejayi had backed into him.
It was Odejayi who had fired the Robins in front after an instantly forgettable first half.
The striker capitalised on sloppy defending by Leo Roget who dithered on the ball instead of hoofing it clear.
Oxford equalised 10 minutes later when Steve Basham brought down Lee Mansell's free-kick with a great first touch and then prodded a shot past Shane Higgs.
Cheltenham similarly protested that this free-kick should never have been given and they also looked to have a point.
The U's then enjoyed a purple patch with substitute Craig Davies twice forcing Higgs into good saves with ferocious long-range shots.
Roget made up for his early blunder with a goal saving tackle on Odejayi as Cheltenham started to come back strongly.
But the tie looked to be heading for extra time until Wilson decided otherwise in the 79th minute.