A Marcos Painter slip allowed the former Motherwell man to slot home left-footed with 20 minutes gone after his initial drive had cannoned back off a post.
The Yorkshire outfit started brightly and saw a stunning Barry Robson dipping volley crash back off the bar after only three minutes.
Bournemouth lacked a cutting edge against the Blades but came close to opening the scoring after eight minutes when the energetic Harry Arter saw a shot cleared off the line by Michael Doyle.
Ryan Flynn thought he had doubled United's advantage late on but his goal was disallowed after a foul in the box from Dave Kitson.
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- Barry Robson