Sheffield United moved up to second in the League One table as Gary Johnson's began with a defeat.
Stephen Quinn's left-wing cross was met by the head of veteran Richard Creswell for the opener.
The hosts had a two-goal half-time lead as Michael Doyle fired home a left-footed low shot from 25 yards.
Lee Williamson scored twice after the break as a rocket into the top corner was followed by a tight-angle finish.
Defender Matthew Lowton had a great chance to score his fourth goal of the season but put his free header wide from Quinn's corner.
Substitute James Beattie also went close but saw his shot saved by Rene Gilmartin, while Jonathan Obika had Town's best chance.
It was the home side's eighth successive home victory in all competitions and their 10th win in 14 matches at Bramall Lane this season.
Yeovil, who reappointed Johnson as manager on Monday, remain in the League One relegation zone, two points adrift of safety.
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Sheffield United boss Danny Wilson told BBC Radio Sheffield:
"I thought we played some great stuff this evening and it was sustained as well.
"We've got enough quality to get goals from other areas than upfront and we've proved it tonight, typified by the left foot strike by Lee Williamson.
"It's another three points, that's all you can look for, but as long as we're picking up points we're in with a chance."
Yeovil manager Gary Johnson told BBC Points West:
"Don't tell me you had a bet on us winning 1-0. That would have been fantastic but unrealistic.
"We said it was always going to be a tough start but it was a good test for me to see which players I think are good enough.
"There's an athleticism you need to compete in this division and Sheffield United showed you what that is."