Paul Coutts and Billy Sharp put the hosts 2-0 up at Bramall Lane at the interval with Roy Beerens pulling a goal back for Reading late on.
The opening goal came in the 19th minute when Leon Clarke's shot was cleared only as far asCoutts, who fired into the roof of the net from 20 yards out.
United increased their lead in the 37th minute when Mark Duffy broke free on the right-hand side of the area and his ball across the face of goal was tapped in by Sharp from close range.
Beerens (85) scored to set up an interesting finish, sweeping the ball home after being set up by Modou Barrow.
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Wilder said: "It was very satisfying. We overcame stubborn opposition, especially at the end, but I thought we were full value for our result.
"The first half performance was up there with one of the best that we've produced all season. We were pretty comfortable after half-time and tried to get a third goal but unfortunately we conceded and gave them a big lift.
"I thought they were only in the game for the last 10 minutes and a little bit at the death, with what the referee put on.
"The key is that you see it out. We want to get up the pitch, but sometimes you can't and you do get pushed back. It's important that you stay solid and tight as a unit, which we did.
"We know there is a hell of a long way to go. We're delighted and we're enjoying the ride."