On-the-whistle report: Sheffield United 2 Rotherham United 0

The midfielder received a straight red card in the 27th-minute after sliding in on George Baldock as he attempted to retrieve possession after a misplaced pas

He will be banned for Wednesday's encounter at Queens Park Rangers, the home clash with Norwich City and the visit after the international break to Derby County

It's a savage blow for the Millers as Vaulks has been a key figure for them all season.

Rotherham had fallen behind to an early goal at Bramall Lane but had worked their way into the game and were enjoying their best spell of the game when their talisman was dismissed.

The visitors were pinned back in the opening exchanges and it was no suprise when they fell behind in the fifth minute, Jack O'Connell steering home Ollie Norwood's corner.

Norwood had already tested Marek Rodak with an inswinging free-kick while Michael Ihiekwe had produced a vital block to keep out George Baldock's shot.

The Millers had a left-off in the 20th minute when David McGoldrick shot narrowly wide after Billy Jones had lost possession.

Rotherham had played their way into the game but their uphill task became even more difficult in the 27th minute when Will Vaulks was sent off.

Then came the contest's  big talking point.

Vaulks got there ahead of Baldock but the challenge was rash and as he walked off he took his long throw, one of his side's most potent attacking weapons, with him.

The opening period ended with Rodak pushing out a Norwood shot and the visitors faced a long second half.

The ten-man Millers battled hard but the absence of Vaulks told and they could hold out for only so long.

In the 64th minute, McGoldrick lofted the ball over the bar when Rodak was off his line and the net was gaping and seven minutes later Rodak beat away a fierce Baldock effort.

A superb Rodak save kept out Enda Steven's 73rd-minute header but seconds later Paul Warne's men fell further behind when Mark Duffy left fly from 20 yards.

All four sides of the stadium rose in the 74th minute to applaud Joan Stewart, the wife of Rotherham chairman Tony, who died earlier this week.

Defeat in the division's early kick-off meant Rotherham would remain third from bottom of the table after the day's remaining fixtures.

Sheffield (3-4-1-2): Dean Henderson; Chris Basham, John Egan, Jack O'Connell; George Baldock, Ollie Norwood, John Fleck, Enda Stevens; Mark Duffy; David McGoldrick, Scott Hogan. Unused: Simon Moore, Richard Stearman, Paul Coutts, Kieran Dowell, Billy Sharp.

Subs: Gary Madine (for Basham, 65), Martin Cranie (for McGoldrick, 84).

Rotherham (4-1-4-1): Marek Rodak; Billy Jones, Michael Ihiekwe, Clark Robertson, Joe Mattock; Semi Ajayi; Jon Taylor, Will Vaulks, Ben Wiles, Joe Newell; Michael Smith. Unused: Lewis Price, Richard Wood, Richie Towell, Jerry Yates.

Subs: Anthony Forde (for Taylor, 69), Ryan Williams (for Newell, 69), Matt Crooks (for Jones, 82).

Goals: O'Connell 5, Duffy 74 (Sheffield).

Referee: Geoff Eltringham (County Durham).

Attendance: 27,402 (2,243).