But managerless Oxford were left kicking themselves because it was the stupid sending off of Jon Ashton which caused their downfall.
Ashton received his second yellow card for obstructing Adrian Forbes in full flow after 60 minutes. He had been booked just ten minutes earlier and presented referee Paul Danson with little option but to produce the red card.
And from the free-kick, whipped over by Forbes, Oxford were caught napping. They clearly had not organised themselves following Ashton's dismissal and although keeper Chris Tardif saved Kevin Nugent's header, Goodfellow followed up to score.
It was not the way to sign off that caretaker manager Darren Patterson was hoping for, as this was expected to be his last game in charge.
Swansea, though, might have been well clear by half time.
Lee Trundle squandered three good chances, having made them all for himself.
He fired into the side-netting after a strong run, curled a shot over the bar from the edge of the box and also hit a shot on the turn just over.
U's striker Tommy Mooney, who went close in the first half with a low drive which flashed just wide, twice nearly equalised.
He had a header saved by Willy Gueret and moments later glanced another header over.
Oxford's best chance was 12 minutes from time when Lee Bradbury had a shot deflected just over by Gueret after a slick one-two with substitute Jamie Brooks.