The Blades scored twice in the first 22 minutes through Mark Duffy and Kieron Freeman before John Fleck added a third with 17 minutes remaining.
Wilder said: “We are moving forward nicely. We know what to expect when we come here and it was really important we started off on the front foot and got the first goal.
“We should have got the first goal after two minutes, we should have got a third after three minutes. For us to get that goal then double it up really gave them a big problem and it was a good afternoon for us.
“I thought there were some really good performances, but the attitude of the team was excellent. We turned up and got our rewards.”
Bolton stay third after this defeat, but the closest they came to scoring was a shot from David Wheater that was cleared off the line shortly before half-time.
Duffy gave the Blades a fifth-minute lead as he stroked home from 12 yards after some good work on the right by Chris Basham.
The visitors, who lost their first two games of the season, doubled their advantage in the 22nd minute when a weakly-struck, harmless-looking cross by Freeman was dummied by Leon Clarke and Ben Alnwick was stranded as the ball crept in at the far post.
Just two minutes after the restart, Alnwick was called into action again as he had to tip over a fiercely-hit 30-yard shot from David McGoldrick, a replacement for Clarke for the second half.
Will Buckley received a yellow card for simulation as Bolton appealed in vain for a penalty.
The hosts then made a double attacking change in the 61st minute that saw Erhun Oztumer and Yanic Wildschut replace Luke Murphy and Buckley.
The Blades remained relatively untroubled as they controlled possession with Basham seeing a low hard shot beaten away by Alnwick. They wrapped up the win in the 73rd minute as Fleck swept home a low cross from Stevens.
Bolton Wanderers: Alnwick, Olkowski, Wheater, Beevers, Grounds, Lowe, Murphy (Oztumer 62), Ameobi, Vela, Buckley (Wildschut 62), Magennis (Donaldson 81). Unused substitutes: Joe Williams, Taylor, Wilson, Matthews.
Sheffield United: Henderson, Basham, Egan, O’Connell, Freeman, Norwood, Fleck, Stevens, Duffy (Stearman 69), Sharp (Woodburn 86), Clarke (McGoldrick 46). Unused substitutes: Lundstram, Leonard, Lafferty, Moore.
Referee: Andrew Madley (West Yorkshire).