Sutton will appear in the last 16 of the FA Carlsberg Trophy for the first time in 13 years thanks to a third consecutive 1-0 win.
Craig Watkins got the only goal to see off Oxford City, and set up a mouth-watering home tie against Wrexham - currently pushing for promotion back to the Football League - on January 12.
United deserved their success on the balance of play, having dominated the first hour, but as so often seems to happen a side is galvanised by going down to 10 men, and after Oxford defender Jack Mills had been sent off with just under half an hour to go, the Blue Square Bet North side put Sutton under increasing pressure.
At the end, having hit the bar twice and seen Kevin Scriven produce a breathtaking save in stoppage time, they were not far from taking the tie back to Oxford, an outcome that appeared a long way away when Mills departed just seven minutes after Watkins had given United the lead their play had deserved.
The first half was mainly one-way traffic, but United could not take advantage of that dominance despite some attractive play on a soft pitch that started slippery but became more reliable as the afternoon went on.
A chance did come after 15 minutes as Michael Boateng, who like Sam Rents was always willing to join the attacks, ran from deep before the ball broke to Harry Beautyman, whose cross was headed wide by a diving Watkins at the far post.
Stefan Payne almost surprised goalkeeper Matt Ingram with a ground shot from all of 25 yards that Ingram pushed wide with difficulty, although he dealt more confidently with a powerful Stephen Old header from the resulting corner.
Having barely been out of their own half in the first half-hour, though, it was Oxford who came closest to the lead from their first corner of the game, the ball falling to the feet of Josh Mulvany who clipped the top of the bar from just inside the penalty area.
There was little change in the pattern of play after the interval, and Sutton finally made their dominance count when Rents, who had an outstanding game, produced a strong run to the edge of the penalty area.
Although the way at first seemed blocked, the ball ran to Tom Kavanagh who neatly avoided two challenges before firing in a low shot that Ingram could only push to one side, and at the head of a queue of onrushing players was Watkins, who gleefully hammered the ball in.
It was a joyous moment, as the celebrations confirmed, although the edge for Watkins was possibly taken off it as he suffered a shoulder injury in the pile-up of players in front of the supporters and had to make way for Marvin Williams 11 minutes later.
By then Sutton seemed well on the way, as Beautyman saw a low shot saved.
Then Mills, booked in the first half for kicking the ball away after it had gone out of play, blocked Harry Ottaway’s run after the striker had done well to anticipate a poor defensive header and received a second yellow card from referee Daniel Cook.
Although United still had chances to make the game safe, Williams, Kavanagh and Craig Dundas going close, it was by no means as straightforward as it had promised to be, and when Dundas lost possession dangerously close to his own penalty area, the luckless Mulvany saw a thumping 30-yard shot go over via the crossbar and also, crucially, Scriven’s fingertips.
The long throws of skipper Andy Ballard were an ever-present threat, Old impressive in repelling the aerial bombardment, but a chance was bound to come from one of them and sure enough, when United failed for once to win the first header, Felipe Barcelos had a close range header and could have been forgiven for starting his celebrations until Scriven managed to spring to his left and claw the ball away one-handed.
Oxford claimed in vain that the ball had crossed the line, but assistant Mark Engelbretson was perfectly placed and had no doubts the save was legitimate, while no-one in the ground could have any doubts that it was something special.
It yielded a string of corners for Oxford and some anxious moments, but for the third game running, United were solid at the back and extended their run without conceding a goal to more than 300 minutes.
Sutton United host Whyteleafe tonight (Tuesday) in the Senior Surrey Cup, before a return to league action at Maidenhead United on Saturday.