A bullet header from captain Neill Collins fired the unbeaten Blades to their first win in four matches - condemning the Glovers to a fourth consecutive league defeat.
In a first half that lacked fluency, both sides created opportunities but lacked a cutting edge in front of goal. Yeovil goalkeeper Marek Stech pushed an early free-kick from Tony McMahon over the bar, before Collins and Paul Gallagher were both denied.
Young midfielder Korey Smith, who completed a three-month loan move to the Glovers from Norwich last week, came closest for the hosts just before the break when his low drive was smartly saved by Mark Howard.
The breakthrough came 10 minutes after half-time when Collins rose highest to head home Gallagher's inswinging corner in front of the jubilant travelling supporters.
The visitors, who drew their previous three matches before arriving at Huish Park, came under little threat as the second half progressed and took home a valuable three points.