Sheffield United: Will Vaulks deserved to walk but Rotherham United will survive, Chris Wilder says

The visitors' captain received a straight red card for a foul on George Baldock midway through the opening period, having conceded possession moments earlier.

Vaulks' sending-off came when as Paul Warne's side were threatening to plot a course back into the game following Jack O'Connell's opener.

Despite paying tribute to Rotherham's performance - "They are a spirited group. They're not going to come here and just roll over" - Wilder revealed: "Everybody at the time thought it was a red. I don't think there was any complaint from Paul either when I spoke to him afterwards."

United, who finished the day in third after briefly climbing to second in the Championship, were forced to wait until the closing stages before extending their advantage; Mark Duffy powering home from long-range after Marek Rodak had made several important saves.

Backing Rotherham to claw themselves out of the relegation zone, Wilder said: "A lot of detail goes into the planning of both teams. They are dangerous and they ask questions of you. 

"We had to be inventive, because they'll just head it clear otherwise. The attention to detail from the players was excellent.

" I never see them (Rotherham) getting beat by four or five. They've got a good attitude and a manager who has done terrifically well. They always make it hard for you."

"We've prepared just as hard for this as any other game," he added, explaining November's draw at New York Stadium had shaped United's approach. "We learned the lessons of earlier this season, when they were better than us and dropped on more second balls. We dealt with what is an effective style of play."