Owusu donned a Terry Butcher-style bandage after picking up a head injury early in the second half.
That did not stop the former Sheffield Wednesday and Brentford striker grabbing the only goal with a bullet header 13 minutes from time.
Swindon striker Lee Peacock had the first sight of goal 21 minutes in, when he was picked out by Sofiane Zaaboub's free-kick but he could only direct his header into the stands.
Christian Roberts called Yeovil goalkeeper Steve Mildenhall into action for the first time six minutes before the interval.
Roberts danced his way past left-back Nathan Jones before unleashing a fierce left-foot shot from the edge of the penalty area, which Mildenhall did well to palm past his left post.
Jamie Vincent came within inches of putting Swindon in front three minutes later when his 30-yard curler shaved Mildenhall's right-hand upright.
Blair Sturrock was presented with another chance in the 44th minute when he headed wide from Vincent's cross.
Yeovil failed to trouble Swindon goalkeeper Phil Smith in a drab opening 45 minutes.
Roberts had the Glovers defence on the back foot again early in the second half when he cut in from right before shooting narrowly over the angle of post and bar from 14 yards.
Terrell Forbes put his body on the line to deny Swindon substitute Simon Cox in the 66th minute when the former West Ham trainee threw himself in the way of Cox's powerful half-volley.
Yeovil took the lead against the run of play when Owusu climbed highest to head home on-loan Manchester United winger Ritchie Jones' corner from six yards.
Substitute Jon-Paul McGovern should have been celebrating a debut equaliser seven minutes from time when he raced onto Zaaboub's pull-back only to blaze over with the goal at his mercy.