The hosts did the damage in the first half before a late Swindon comeback reduced the arrears.
After an even opening, the home side went in front. A Town corner was cleared out to the wing where the Oxford wide-man skipped away from a challenge before sliding the ball across for the advancing AJ George. One-on-one with Town 'keeper, Aaron Moody, the U's striker found the bottom corner of the net.
Shortly afterwards, Oxford doubled their money. Ryan Wood brought down George in the box and the striker picked himself up then fired home from the spot.
Scott Lindsey's side did create chances of their own: Jake Evans stung the palms of Jack Stevens in the Oxford goal while skipper, Lee Marshall, having scored directly from a corner in the last round, cracked the outside of the post with an in-swinging delivery. Callum McCorrmack also tested Stevens with a well-struck effort from distance.
Just before the break, Oxford made it three with George grabbing his second of the evening. Some neat work from Muctaru Conte on the left created the chance with his cross picking out George in the box. The striker did the rest, heading in past Moody.
The pattern of the second half saw Swindon enjoying a lot of possession with the home side looking to break on the counter-attack. After Marshall had brought a neat save from Stevens, Town almost conceded a fourth. George snaffled possession from Moody and set his sights on the open goal. With just Tom Smith between him and a hat-trick, the striker sliced his effort wide of the target.
Will Randall's shot in the 70th minute looked set to hand Town a way back into the match but a defender on the line hacked the ball away from danger.
As the game entered its final ten minutes, Swindon did eventually make the breakthrough. Some fine work from Randall on the left ended with him squaring the ball across the face of goal where McCorrmack arrived to side in at the far post.
Three minutes later, Town netted a second. Tommy Ouldridge, one of Swindon's Under-16s, found some space on the edge of the box and drove the ball through a crowd of players and into the net to set up a grandstand finish.
Unfortunately, the final chance never came for the Town, leaving manager Scott Lindsey to reflect on what might have been.