United moved back into the Sky Bet Championship automatic promotion places, for the time being at least, as they beat 10-man Millers.
Jack O'Connell's opener and Mark Duffy's fifth goal of the season ensured a comfortable victory for the Blades after Rotherham captain Will Vaulks was sent off in the first half.
The hosts recorded a fifth successive clean sheet with Dean Henderson largely untroubled in goal as he took his season tally to 15.
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And Wilder said: “They were stubborn opposition and we prepared as much as we have for any other game this year.
“We learned the lessons of what happened at the New York Stadium [a 2-2 draw earlier in the season] because they were better than us that day and outfought us as well.
“It was a game of two different styles, which I have no issues with because I played in a style that was effective, and they ask questions.
“We had to answer them, especially defensively. Dealing with long throws and corners.”
O’Connell got United off to a flying start with the opener in the fifth minute before Duffy netted a left-foot screamer in the second half.
“We started tremendously and got an early lead, and had good chances before that too,” Wilder added.
“The sending-off gave us a numerical advantage, and as we’ve seen before it’s not always easy when a team sits as deep as that.
“We had to be patient, thankfully we were and got the right result.”