The only goal of the game came just before half-time, when former Oldham striker Chris Porter headed home for the visitors.
The Blades took the lead when Richard Cresswell picked up Matthew Lowton’s long ball and crossed to Porter, whose header helped the ball over the line.
Yeovil created a good chance when Alan O’Brien’s left-wing cross evaded Gavin Williams at the far post.
Terry Skiverton’s side were reduced to 10 men when Curtis Haynes-Brown was sent off for a second bookable offence.
“It was a very determined performance and it was a physical game,” said Blades boss Danny Wilson.
“The one thing we did have to do was defend and defend solidly.
“I think there were times where we could have broke the play up a little, but that’s a minor thing we can work on.”
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