Last updated on .From the section Championship

Will Vaulks was sent off just days after signing a new contract for next season with Rotherham

Sheffield United continued their push for automatic promotion with a seventh successive home win as they beat 10-man Rotherham United at Bramall Lane.

Defender Jack O'Connell gave the Blades the perfect start by turning in Oliver Norwood's clever low corner as the Rotherham defence was slow to react.

The long throws of captain Will Vaulks looked a likely way for Rotherham to conjure a reply, but that threat disappeared when he was sent off for a late tackle on George Baldock.

Chris Wilder's side dominated a second half played in driving rain and, just seconds after Marek Rodak made a superb save to keep out an Enda Stevens header, the keeper was beaten by Mark Duffy's strike.

The victory made it eight games unbeaten for the Blades and lifted them back up to second in the Championship, although they later reverted to third after Leeds won at Bristol City.

The Millers went into the South Yorkshire derby unbeaten in six matches - albeit with only one win and five draws in that run - but the odds were stacked against them once Vaulks was punished for his rash challenge after a loose pass.

Their players wore black armbands in memory of chairman Tony Stewart's wife Joan, who died earlier this week, and there was applause for her from all sides of the ground in the 74th minute.

Rotherham did not manage a single shot on target and Rodak was kept busy with saves to deny John Fleck, Norwood and David McGoldrick twice, as well as Stevens

Duffy, however, gave Rodak no chance with a shot into the top corner for his fifth goal of the campaign.

Rotherham's defeat meant they remained third from bottom of the table, a point behind Millwall.

Jack O'Connell's goal was only his second of the season for Sheffield United

Sheffield United manager Chris Wilder:

"They're stubborn opposition so we prepared just as much as any other game this year.

"It was two different styles today, it's back to front for them and it's effective. They ask questions so I am delighted that we answered those questions defensively.

"We started the game in a tremendous fashion and obviously we got an early lead after a couple of good chances before then.

"It was difficult because they sat in and at times maybe we tried to be too precise but we were always looking to get a second goal."

Rotherham boss Paul Warne:

"We're not a dirty team. I think Will is just really competitive, he plays with his heart on his sleeve and that's why he is so good for us.

"I don't think he has gone into the tackle with any intent to hurt the lad but obviously his exuberance meant it was a red.

"The lads put in everything they've got, I've got no complaints at all and I'm proud to be their manager.

"Two-nil away from home doesn't sound like a great result but goal difference is key for us. It could have ended up being a lot more so overall I've had better days but I've had worse."