United's 125th birthday celebrations were somewhat dampened by a defeat to the Sky Bet League One leaders.
United's 11-match unbeaten run was broken after goals in each half, from James Henry and Dave Edwards, secured the points for Wolves.
On a day of celebration, 125 years to the day that the Blades were formed, Nigel Clough's side battled but were undone by the division's top side.
Brayford returned for the fixture with the leaders, he replaced the injured Harris and was United's only change from the midweek draw with Preston - 18-year-old Academy prospects Khan and Dimaio were on the bench. For Wolves, former Blade McDonald started.
As he finished the game at Deepdale, Freeman started at left-back and with the vocal backing of the Lane, the Blades made a very positive start. Just four minutes had elapsed when Murphy's cross was touched by Baxter for Scougall to shoot, which was pushed away by Ikeme.
Jacobs dinked past three tacklers and fired at Howard before the visitors took the lead, fortuitously, on 13 minutes. HENRY delivered a cross from the right and the run of Edwards took the attention of Howard, allowing the ball to drop into the corner of the net.
The Blades attempted to hit back immediately, a Baxter free-kick deflected into the arms of Wolves' goalkeeper and there was a penalty appeal turned down when Batth, already booked, blocked the run of Coady.
Wolves went close to doubling the lead when Henry robbed Maguire and fired against a post, whilst they also had an appeal for a penalty when Maguire and Jacobs clashed but again referee Friend said no.
The strong arm of Ikeme kept out Baxter's shot on 36 minutes and the Blades were continuing to force the issue. On 44 minutes a Baxter corner was flicked on and Brayford's effort at the back post was headed off the line by Stearman, whilst before the ball was cleared, Collins was bundled over in the box but again there was no whistle, well, not until the half-time signal moments later.
Like the first half, the Blades created a chance four minutes into the second period. This time Brayford's cross was controlled by Murphy and Scougall fired over. Wolves then took advantage and doubled their lead on 53 minutes, Henry's low cross was deflected by Doherty and EDWARDS converted with a right-footed effort.
Baxter clipped the side-netting with a 25-yard free-kick and Davies took over from Flynn, whilst Clarke wasted two good chances for the visitors - he strayed offside when converting Henry's cross and then shot over after good work from Edwards.
Porter was introduced for Baxter and the Blades continued to battle. Murphy's effort was deflected wide after Maguire's burst out of defence and a Porter header was collected by Ikeme.
Paynter replaced Freeman for the closing stages as United looked to get back in the game but five minutes of added time only could herald two penalty appeals but referee Friend remained consistent and awarded nothing.
Blades: Howard, Brayford, Maguire, Flynn (Davies 62), Doyle, Baxter (Porter 66), Collins, Coady, Scougall, Murphy, Freeman (Paynter 88).
Unused: McGinn, Long, Khan, Dimaio.
Wolves: Ikeme, Doherty (Ricketts 75), Edwards, Stearman, Batth, Henry, Clarke, McDonald, Evans (Price 62), Golbourne, Jacobs (Sako 90).
Unused: Elokobi, McAlinden, McCarey, Dicko.