Ruben Rodrigues had taken advantage of some slack defending to give United the lead just before half an hour had been played, but Sinclair Armstrong netted shortly before the hour, while Nahki Wells scored from the penalty spot in the final quarter of an hour.
Des Buckingham made just the one change to the side which beat Stoke City 1-0, with that enforced as the injured Cameron Brannagan missed out. Rodrigues came into the starting line-up.
Haydon Roberts had the first sight of goal when he saw a deflected strike fly over the crossbar, while Zak Vyner directed a wayward header over from a right-wing free kick.
Anis Mehmeti then drifted infield and sent a fizzing effort into the midriff of Jamie Cumming, before a great chance was presented to Armstrong.
The striker’s glanced header from a left-wing Roberts cross whizzed just wide of the far post though.
Straight away at the other end, Greg Leigh sent in a teasing ball and Tyler Goodrham arrived at the back post, but sidefooted his effort over.
Scott Twine was the Robins danger man, and his clever through ball found the run of Mehmeti, who shot straight at Cumming with 20 minutes on the clock.
A brilliant minute’s applause from the U’s faithful, in tribute to Jack Badger, was held after 24 minutes, and shortly after, Mehmeti got down the right channel and tested Cumming at his near post.
United though took the lead not long later. Siriki Dembele drove at the Robins backline and saw a 20-yard strike deflect into the air.
Rodrigues followed the flight of the ball and ran beyond the static home defence, allowing the midfielder to tap in past Max O’Leary.
A nice run from Peter Kioso then found Rodrigues, who pinged in a crisp through ball for Mark Harris, who saw a low strike saved with relative comfort.
Robins skipper Jason Knight headed over at the near post from an inswinging Twine corner, while Armstrong thumped a header wide moments later.
With four minutes to go until the break, the U’s were inches away from doubling their lead.
Dembele again drove forward, and this time, he smacked a 25-yard strike against the top of the crossbar.
Buckingham was handed an injury blow just before the break, as Josh McEachran picked up a knock, and Will Vaulks came on in his place.
Twine started the second period as he played the first, and four minutes after half-time, he ran into space and sent a dipping 25-yard strike over the bar.
A deflected effort from Armstong inside the penalty area was then claimed by Cumming.
Harris had a great opportunity to get on the scoresheet 10 minutes into the second half, after Rodrigues sent in a teasing ball across the six-yard box, but Harris got his connection wrong and stabbed wide from close range.
It proved costly, as the Robins found a leveller almost straight away at the other end.
Knight played a low cross in from the right, and Armstrong found the bottom left corner from the centre of the box.
Twine sent a 20-yard free kick that he won himself, before Buckingham made his second alteration.
Dane Scarlett replaced Rodrigues, a switch which saw Harris move out to the right, Goodrham come into midfield, and Tottenham Hotspur loanee Scarlett go up front.
The Robins took the lead in the 76th minute following the award of a soft-looking penalty.
Harris was adjudged to have fouled Roberts, with referee Will Finnie taking a moment to make the call.
Wells, on as a substitute for Armstrong, made no mistake from the spot though, hammering the ball home from 12 yards.
With nine minutes to go, Buckingham made a double switch on the wings, as Kyle Edwards and Malcolm Ebiowei replaced Dembele and Goodrham, as Harris moved infield.
For Edwards, it marked a return to the pitch for the first time since the end of November, having recovered from a succession of hamstring injuries.
Bristol City (4-2-3-1): O’Leary; Tanner, Vyner, McNally, Roberts; Williams (Hirakawa 46), Knight; Mehmeti (Pring 89), Bird, Twine; Armstrong (Wells 64).
Unused subs: Bajic, Naismith, Mayulu, Sykes, Cornick, McGuane.
Booked: Williams.
Oxford United (4-3-3): Cumming; Kioso, Moore, Brown, Leigh; Rodrigues (Scarlett 68), McEachran (Vaulks 44), El Mizouni; Goodrham (Ebiowei 81), Harris, Dembele (Edwards 81).
Unused subs: Ingram, Nelson, Long, Sibley, Dale.
Booked: El Mizouni, Brown, Moore, Vaulks.
Referee: Will Finnie (Bedfordshire)
Attendance: 24,807 (TBC away)