The Blades were dominant in picking up three points against old foes Bolton Wanderers.
Mark Duffy set the tone with a goal on five minutes and further strikes from Kieron Freeman and John Fleck sealed the points.
Wilder's team showed one change with Duffy, available again after illness, taking his place in the starting line-up. Woodburn dropped to the bench. It proved to be a good move as United made a blistering start.
It took less than 30 seconds for the Blades to create a chance. After linking up with Sharp, a right-foot effort from Stevens was blocked by Wheater. From the resulting corner, a short Norwood pass found the run of Fleck but Alnwick pushed the midfielder's shot onto the crossbar. Referee Madley checked his technology but this week the Blades players' appeals were not rewarded.
The opening goal, though, arrived on five minutes. Bolton had a corner that amounted to nothing but United's start was deservedly rewarded. All that was left was for DUFFY to slide the ball into the bottom corner from Basham's lay-off after the home side failed to clear Fleck's crossfield pass to Freeman.
Basham was back on defensive duty to prevent Wheater or Magennis getting on the end of Ameobi's cross and Buckley's fall in the box did not convince the referee as Bolton looked to get on level terms.
Clarke's intelligent ball through the defence almost put Sharp in but Olkowski cleared at the expense of a corner, from which Basham fired wide.
The away side was clearly on top and a second goal followed on 22 minutes, in bizarre circumstances. Clarke laid off to FREEMAN, whose low, precise side-foot cross crept in via the back post after Clarke continued his run to put off Alnwick and his defenders.
Fleck got the better of Lowe and attempted an audacious chip which looked to have beaten Alnwick but the ball landed on the roof of the net.
Late in the half Bolton forced United back but the best of their set-pieces saw Wheater's effort kicked off the line by Clarke in a crowded penalty area.
McGoldrick replaced Clarke at the break and was close to making an instant impression but goalkeeper Alnwick back pedalled to tip over the substitute's long-range effort.
Scorer Freeman was heavily involved in the second half. He opted to pull back to Sharp instead of shooting and the skipper's effort was blocked; then Freeman half-volleyed wide after Norwood won possession deep in Bolton's half.
In a rare Bolton attack, Magennis headed wide a Wildschut cross and Stearman was added to the defence as an insurance policy. However, the Blades were still in control and a great turn by Basham almost got him a goal against his former club but Alnwick parried away.
On 73 minutes, though, a Blades third goal finally ended any Bolton hopes of mounting a fight-back. Once again, the visitors committed players forward and from a low Stevens cross, FLECK turned the ball home at the near post.
There were opportunities for further goals. A ball over the top found Sharp, who shot wide; whilst Freeman found himself clear on the right but his effort was deflected away for a corner.
Woodburn was introduced late on and Bolton attempted a number of long-range efforts - twice Ameobi failed to find the target - before the referee's final whistle gave the green light for the players and 1,978 Blades fans inside the stadium to celebrate.
Bolton: Alnwick, Lowe, Beevers, Vela, Ameobi, Buckley (Wildschut 56), Murphy (Oztumer 56), Olkowski, Magennis (Donaldson 81), Grounds, Wheater.
Unused: Taylor, Wilson, Matthews, Williams.
Blades: Henderson, Stevens, Fleck, O'Connell, Basham, Clarke (McGoldrick 45), Sharp (Woodburn 86), Egan, Norwood, Freeman, Duffy (Stearman 69)
Unused: Lundstram, Leonard, Lafferty, Moore.