Goals from Jack O'Connell and Mark Duffy - either side of Will Vaulks's first-half red card - saw the Blades maintain their top-two challenge.
The Blades made four changes, after Monday’s Steel City derby, with David McGoldrick and Scott Hogan in attack. Mark Duffy and George Baldock also came in.
Rotherham made two changes, Ben Wiles and Joe Newell in. Richie Towell and Anthony Forde dropped to the bench.
Goalkeeper Marek Rodak was not punished after spilling Ollie Norwood's free-kick, then Baldock's goal-bound effort was blocked.
So it was no surprise when Chris Wilder's men took the lead, but it was poor defending from the visitors.
Norwood's corner was low, and O'Connell - so often a danger at set-pieces - was given time to side-foot the ball into Rodak's left-hand corner.
Rotherham's first effort on goal was a long-range strike from young midfielder Wiles, that was comfortable for goalkeeper Dean Henderson.
But the hosts had a good chance to make it 2-0, but McGoldrick dragged his shot wide, while Rodak held a fierce John Fleck shot.
Rotherham enjoyed a decent spell of possession, but their task got harder when midfielder Vaulks was shown a straight red card after 28 minutes. The Millers man gave possession away, and attempting to win the ball back, dived in late on Baldock near the halfway line.
Despite the loss of their captain - who now faces a three-match ban - Rotherham remained in the game as they got through to half-time with just a one-goal deficit, Rodak saving from Norwood in first-half stoppage time.
The Millers goalkeeper was also well placed to keep out McGoldrick, after the break, as the Blades struggled to break down stubborn opposition, with striker Michael Smith a lone figure up front for the visitors.
Rodak was having a busy afternoon, and after Rotherham were caught in possession, the Millers 'keeper did well to thwart McGoldrick in a one-on-one, before the United striker poked the ball over the crossbar.
Wilder brought on an extra striker in Gary Madine, in place of defender Chris Basham, as they looked for the killer second goal.
Warne responded by bringing on extra legs in midfield, Forde and Ryan Williams replacing Newell and Taylor.
Baldock was next to try his luck, but Rodak parried away his long-range strike, before denying Enda Stevens's header.
But Rodak could do little to prevent Duffy making it 2-0, the Blades midfielder firing high into the net at the Kop end.
The Millers saw penalty appeals waved away after Clark Robertson went to ground in a rare Rotherham attack.
United came close to a third, when Fleck's shot was blocked - after another well-worked low corner which caught out the visitors.
And virtually with the last touch of the game, Rodak had the final word, keeping out Baldock's shot on the line.