Jermaine Johnson struck with 18 minutes remaining and Tommy Miller added a second from the penalty spot to seal the points.
Owls defender Jon Otsemobor was sent off for a professional foul late on but the damage had already been done.
Yeovil had some half chances early on but the best opportunity in a goalless first half fell to Gary Teale in the 10th minute. The winger had a clear opportunity got on the end of a right-wing cross Clinton Morrison but side-footed over the bar.
Johnson came on midway through the second half and after 71 minutes he unleashed an unstoppable drive into the far corner from the edge of the box. The Owls then clinched the game from the penalty spot after 82 minutes. Luke Ayling brought down Otsemobor and Miller sent keeper Stephen Henderson the wrong way.
There was late drama when Otsemobor was dismissed for a foul on Nathan Smith but the Owls were not to be denied all three points.