A debut goal for Spurs loanee Cameron Carter-Vickers was enough for the Blades to secure another victory on the road.
He struck in the first half in a battling display at the Macron Stadium.
Boss Wilder freshened the Blades team after a hectic start to the campaign. Carter-Vickers made his debut and Clarke returned after suspension. Wing-backs Baldock and Lafferty also started. Donaldson missed out through injury, whilst Freeman, Stevens and Basham, the latter suffering with a minor muscle injury, dropped to the bench. Coutts, meanwhile, made his 100th start in the Blades shirt.
A frenetic opening ten minutes was even in terms of possession, territory and chances. For Bolton, Karacan's goalbound effort was headed away by Wright and Sharp's shot was on target but blocked by Wheater.
Duffy found space and Baldock and Lafferty were quickly involved in the action but the neat intra-play around the Bolton box failed to create a worthwhile chance. On 22 minutes, a weak Madine effort was comfortable for Blackman.
United, though, took advantage of the first corner of the night to open the scoring. Coutts delivered, a header back from O'Connell forced a melee and CARTER-VICKERS jabbed the ball home at the second attempt, with the aid of a post.
After few chances early on, there were opportunities as half-time approached. The next fell to the home side when Little got the better of Lafferty but from Armstrong's shot on the turn, Wright again headed away.
With the final chance of the half, Carter-Vickers went mightily close to adding a second on 42 minutes, from a Duffy free-kick, but the defender's close-range effort was saved and held by goalkeeper Alnwick.
The rain of the first half continued as the second period kicked off but it did not deter the energy levels of both sides. For Bolton, Karacan half-volleyed over after Madine nodded down and Lafferty's header was cleared off the line by Wheater following impressive link up play on the right by Duffy, Baldock and Coutts.
As Bolton lumped more balls into the penalty area, Blackman commanded his box, whilst Lundstram was United's first change, replacing Duffy, followed by Brooks taking Sharp's place.
As the final ten minutes approached, the pace of the game remained quick. Carter-Vickers was adjudged to have fouled Madine but the resulting free-kick from Morais was too high.
Coutts poked wide for United but a number of late free-kicks allowed Bolton to continue to pepper the Blades box - O'Connell, Clarke and Wright all headed clear at different intervals, whilst Blackman came off his line again to claim from Morais.
Basham replaced the tiring Baldock and a cheap foul by Madine played into United's hands as it wasted more seconds.
Five minutes added time was the sign for Bolton to add some of their defence to the attack. More lumps into the box gave Blackman more catching practice and with the home side leaving holes, Lundstram raced clear but his effort came back off the crossbar - no matter, the victory was confirmed seconds later.
Bolton: Alnwick, Little, Beevers, Karacan, Buckley (Morais 30), Madine, Robinson (Wilbraham 76), Cullen, Armstrong (Le Fondre 67), Wheater, Burke.
Unused: Dervite, Noone, Pratley, Howard.
Blades: Blackman, Baldock (Basham 87), Fleck, O'Connell, Clarke, Sharp (Brooks 73), Wright, Coutts, Carter-Vickers, Duffy (Lundstram 64), Lafferty.
Unused: Stevens, Freeman, Eastwood, Evans.