David Nugent, watched by Everton manager David Moyes, had a great chance after seven minutes when Adam Nowland put him clean through, but Blades keeper Paddy Kenny saved his 18-yard shot.
David Jones, on-loan from Manchester United, then had a 20-yard free-kick saved by Kenny after Tyrone Mears had been fouled, as the hosts enjoyed the better of the opening stages.
United improved as the first half went on and after 30 minutes Danny Webber's 20-yard shot was deflected for a corner.
Just before half-time Sheffield captain Phil Jagielka saw a 20-yard drive saved by Carlo Nash.
Jagielka had another chance to break the deadlock early in the second half but volleyed over from just inside the area.
Nugent did his best to break the deadlock but his closest effort was a half-volley that flew just wide of the target.
Late on home substitute Lewis Neal smashed a 25-yard drive wide of the right-hand upright and a game that neither side deserved to win finished in stalemate.