The 23-year-old Irishman struck seven minutes before half-time, after Birmingham teenager Nathan Redmond had scored against the run of play in the 18th minute.
Birmingham never looked back after Rooney had added that second goal, and although the Blades struck the woodwork twice in a matter of seconds shortly after the restart, Wade Elliott added a third for the Championship side and Rooney wrapped up the contest in the 78th minute to end the Blades' eight-match winning run at home.
Danny Wilson's Blades are flying high in League One as they bid to bounce straight back to the second tier.
But they were no match for Chris Hughton's in-form side, who have now won their last five matches and are unbeaten in their last nine.
The home side were unchanged for the fourth game running, while Hughton recalled goalkeeper Colin Doyle, midfielders Morgaro Gomis, Redmond and Elliott, plus striker Rooney.
The tie's opening chance fell to the Blades in the fourth minute. Full-back Matt Lowton crossed from the right and midfielder Kevin McDonald's well-struck shot from the edge of the penalty area was blocked by defender Curtis Davies.
Ched Evans was next to threaten as United made all the early running, but Birmingham shocked them by taking the lead.
Midfielder Jordon Mutch swung over a corner from the right and when the ball broke to Redmond on the edge of the penalty area, the 17-year-old rifled home a low shot into the centre of goal.
Redmond fired another effort just wide when cutting in from his wing five minutes later as the visitors seized the initiative, but Blades striker Evans forced Doyle into a smart save with a 20-yard free-kick in the 27th minute.
Full of confidence, Redmond tried his luck from further out, but his 30-yard rocket was just off target, while Evans lashed a volley wide from a similar distance.
But, buoyed by their initial breakthrough, Birmingham carried all the momentum and when they doubled their lead through Rooney it was no more than they deserved.
Winger Chris Burke waltzed into the penalty area and played the ball square for Rooney to lash home his fifth goal of the season, high into the net from six yards.
The Blades had chances to get back into the game seven minutes after the restart but luck was not on their side.
Lee Williamson's crisp shot from inside the area hit the crossbar and Lowton's follow-up effort also came back off the woodwork with Birmingham goalkeeper Doyle well beaten.
But it was not to be United's day and Elliott rubbed salt into their wounds when thundering home the visitors' third goal from 20 yards five minutes later.
Rooney sidefooted home the fourth goal following David Murphy's cross.