Chris Hackett scored two goals in a game for the first time in his career after being switched up front from the wing as United showed they could win without Tommy Mooney.
Leading scorer Mooney was axed, along with Juan Pablo Raponi, but the team appeared none the weaker.
With Bradbury giving a masterful exhibition, the U's equalled their biggest away win of the season and recorded their first double.
Hackett took his chance superbly. His pace destroyed Mansfield's sluggish defence and every time the ball was played over the top he was quickest to it.
But while Hackett had the most impact on the game, Bradbury was its outstanding player.
The skipper returned from suspension and was superb on the right side of midfield, his quality first touch and perfectly weighted passes providing Steve Basham and Hackett with the service they wanted.
Bradbury set the tone for a first half, controlled by the visitors, with a brilliant pull-down to control the ball and beat his marker, his curling left-footed shot then deflecting for a corner.
It was good play by Hackett which set up Oxford's opening goal in the eighth minute.
He outwitted Adam Rundle by heading the ball on and sprinting forward. And Basham, finding himself in space because Rhys Day was slow to come out, turned the defender and fired home left-footed.
Former England youth midfielder Adam Murray struck a powerful 25-yard strike, which Chris Tardif got right behind, but after that the visitors took over.
Hackett made it 2-0 on 33 minutes with a clever lob over goalkeeper Kevin Pilkington after Robinson had set him clear with a right-footed chip.
Bradbury continued to make Rundle look stupid with his silky skills. With Mansfield surprisingly persisting in trying to play offside, despite being so bad at it, further chances came Oxford's way.
At the other end, Jon Ashton got away with an unconvincing passback to Tardif when under pressure. After what had happened last season, one would have thought he'd have known better.
Just before the break, Basham had another goal disallowed for an apparent push on the keeper, which seemed a harsh decision.
Mansfield boss Carlton Palmer had made five changes to his side, with right back Scott McNiven making a surprise but welcome return against his former club.
McNiven was made skipper for the day but must have been embarrassed by his side.
They looked as poor a team as United have faced this season and Palmer was booed off when he made his way to the dressing rooms at half-time.
Despite having surrendered a first-half lead three times in the past two months, there seemed little prospect of that this time and Horacio Rodriguez's men continued to attack with pace.
Basham had an angled shot saved after brushing off a weak challenge from Alex Neil, but three minutes into the second half Hackett pounced again.
The ball came off the head of centre back Day and Hackett was on it in a flash. He sprinted forward and coolly slotted past the keeper and into the bottom right corner.
Mansfield's reply was an Andrew Barrowman volley which cleared the bar by eight yards.
The U's were now happy to play on the break, and they continued to look dangerous.
Craig Davies replaced Basham to provide United with two pacy attackers. They should have scored another, but Davies delayed his pass a fraction too long and Hackett was caught offside.
In the closing minutes, Tardif had to save from Luke Dimech.
It should have earned him a clean sheet, but Ashton wrecked that with a stupid challenge on Simon Brown to give away a penalty.
Tardif saved the 90th-minute spot-kick from Colin Larkin, but the assistant referee signalled that he had moved off his line, and Larkin sent him the wrong way with the retaken penalty.
It was an annoying end for United, who still can't get out of the habit of giving away stupid second-half goals.
But at least they won this time.
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