Sheffield United secured their first victory in four attempts against a Yeovil side who have now lost four on the bounce.
There were few chances in the first half, but Neil Collins headed home Paul Gallagher's inswinging corner to settle the match after the break.
Glovers keeper Marek Stech kept out further efforts from Collins, Gallagher and Tony McMahon.
Korey Smith's low drive was the closest the home side came to a goal.
VIEWS FROM THE DRESSING ROOM
Yeovil Town manager Gary Johnson told BBC Somerset:
"I thought the lads gave it a right go and we kept the ball against a decent team.
"People are going to shoot me down because it's a defeat but we played well.
"I thought we did enough to get something out of a very strong team.
"They are very clever and that's why they get paid a lot more money than we do."
Sheffield United manager Danny Wilson told BBC Radio Sheffield:
"It was a very strong and determined performance.
"After the early part of the game they (Yeovil) had a few half chances, where we scrambled and Mark Howard came to our rescue on one or two occasions.
"We could have done better in front of goal, but three points at this stage of the season are paramount to keep the momentum going."