The Blades were ahead in the fifth minute when leading goalscorer Ched Evans got clear on the right and his low centre was turned over the goalline by Bournemouth captain Adam Barrett.
Bournemouth might have been further behind in the 10th minute when Richard Creswell went around goalkeeper Darryl Flahavan, but saw his effort cleared off the line by Simon Francis.
Bournemouth lost defender Shaun Cooper with an injury in the sixth minute and the nearest they came to equalising was a left-footed shot from Michael Symes, which flashed past the post.
Bournemouth made big efforts to equalise in the second half, but Sheffield United’s defence held firm under pressure.
The visitors broke in the 74th minute when Evans again got clear on the left and another low centre was touched over the goalline, this time by Bournemouth defender Steven Cook under pressure from Creswell and apart from Barrett’s header, which visiting goalkeeper Steve Simonsen held under the crossbar, the Blades had a trouble-free second half.