James Henry opened the scoring at Bramall Lane when his 13th-minute cross from the right evaded Blades goalkeeper Mark Howard and crept inside the far post before fellow midfielder Dave Edwards sealed the win with a close-range finish eight minutes after the restart.
Henry also hit a post with a first-half strike, while the home side went close through Stefan Scougall's early drive, which was saved by Wolves goalkeeper Carl Ikeme, and John Brayford's attempt, which was cleared off the line by Richard Stearman on the stroke of half-time.
"It was a fantastic win, I felt we needed to make some changes and we needed some fresh energy in the team," Jackett said.
"On Tuesday night (the loss to Crawley) we didn't quite have as good energy and legs as we usually have and we really needed it today on a big pitch against a very good footballing side with the best part of 22,000 people here.
"I do have confidence in the players coming in that they know their roles. It's a big game to come in for but there's no point them being there if I don't think, at the right time, they can come in and give us some fresh energy.
"I thought as the game wore on we handled Sheffield United better and better. Some of their football in the first half was very, very good - as was ours - and I thought two quality teams and two quality clubs."