Hosts Wigan gave as good as they got for the first half-hour, and should have led only for Lee Evans to squander a gilt-edged opportunity from bang in front of goal.
David McGoldrick put the Blades ahead five minutes before half-time, and goals from Mark Duffy and Billy Sharp within nine minutes of the restart made the game safe.
“I was pleased with the second half, not so much the first half,” admitted Wilder.
“It was a pretty slow start and I thought we were a bit fortunate to go in at half-time 1-0 up.
“They obviously missed a great chance that maybe affected them a little bit. Then we get the goal and we don’t look back.
“What Wigan are going through now, when things aren’t going for you, is similar to what we went through last year.
“You’re just looking for something to give you a lift, but thankfully for us it didn’t come today.”
Wilder made only one enforced change from the win over Blackburn but revealed he had given his team selection a great deal of thought at the end of a hectic festive programme.
“We’ve obviously had a lot of games in a short space of time, and I was massively thinking of freshening it up,” he added.
“But the attitude of the players in the last few days showed me there were desperate to go again.
“We maybe lacked a little bit of our zip and energy, but we felt if we could raise the bar we could take the game away from our opponents – and that’s what we did.”
For Wigan boss Paul Cook, there was no respite from a gloomy period that has seen them win only once in the last 13.
Apart from Evans’s shocking miss, the home side created very little for lone striker Joe Garner.
“You have to give them a lot of credit, they are a fine team,” said Cook. “But it’s just not going for us at the minute.”
Wigan Athletic: Walton, James, Kipre, Dunkley, Naismith, Gibson (Windass 51), Massey (McManaman 51), L Evans, Morsy, Roberts, Garner (Grigg 78). Unused substitutes: Byrne, Vaughan, Jones, Connolly.
Sheffield United: Henderson, Cranie (Stearman 80), Egan, O’Connell, Baldock, Norwood, Fleck, Stevens, Duffy (Coutts 66), McGoldrick (Clarke 74), Sharp. Unused substitutes: Freeman, Johnson, Moore, Washington.
Referee: A Madley (West Yorkshire).