Two second half goals from Billy Sharp and defender James Wilson turned the game on its head at Bramall Lane.
Newly-promoted Oxford, a former side of Blades boss Chris Wilder, had taken the lead in the 16th minute through Kane Hemmings' header.
The win ends United's worst start to a season for more than 20 years and moves them up to 20th in League One, two places below the visitors.
Assistant boss Alan Knill said: "We told them they were playing well, and to keep going.
"We had great chances in the first half that we didn't take but if we kept believing, it would come.
"And then when it did... Wow.
"What a crowd and what a ground. Get that goal and the crowd were unreal and from then, there was only going to be one winner. "