John Brayford opened the scoring for Nigel Clough's side before Ryan Flynn combined with Jamie Murphy to double the advantage.
United, who climbed above the Robins in the table, sealed maximum points courtesy of Jose Baxter's penalty as City, who barely made an impression on the match, were left to reflect on a potentially costly afternoon.
The Blades dominated the opening period but we forced to wait until the 43rd minute before taking the lead.
Wade Elliott's shot, which flew safely wide of Mark Howard's far post, proved to be a rare moment of promise for City who from that moment on found themselves struggling to contain the hosts.
Aden Flint was forced to hack clear off the line after Murphy, one of the stars of United's march into the FA Cup quarter-finals, pressurised Simon Moore into a mistake as they contested a looping high ball before fellow winger Flynn swept a shot inches wide from an acute angle.
Harry Maguire appeared destined to break the deadlock after powering through to the edge of City's six-yard box but Jay Emmanuel-Thomas bravely flung himself in front of a fierce shot.
A feature of United's play under Clough has been their ability to wreak havoc down the flanks. So, with compatriot Stefan Scougall asked to drive beyond lone striker Jose Baxter at every opportunity, it was no surprise to see the two Scots continue to feature at the heart of United's best moves.
But Brayford, on loan from Cardiff, was responsible for handing United the lead when he fired home after Maguire had helped on Baxter's corner.
The visitors, aware of the afternoon's significance, looked a much more cohesive unit at the start of the second half. But again it was United, this time through Bob Harris, who came closest to scoring when his free-kick was saved by Moore.
However, he was powerless to prevent Flynn from doubling the advantage just before the hour after the ever-threatening Murphy had ghosted past Karleigh Osborne and found his colleague on the edge of the box.
The hapless Osborne was responsible for conceding the foul on Flynn which allowed Baxter to convert from the spot in the 70th minute.
Mark Howard denied Elliott and Sam Baldock with a fine double save during the closing stages.