In the 76th minute with Yeovil clinging to a one-goal lead, central defender Skiverton failed to reach goalkeeper Asmir Begovic with a back pass.
Alert Jabo Ibehre, who was making his debut after a move from Leyton Orient, slipped the ball under the goalkeeper to save the day for the Saddlers.
The match started brightly for Yeovil. Budget restrictions means they had to trawl some of the lower leagues for talent and boss Russell Slade appears to have found a winner in Gavin Tomlin, who scored 24 goals for Fisher Athletic in the Blue Square League last season.
It took Tomlin just ten minutes to open his Yeovil account. Busy Paul Warne powered in a shot which was blocked by goalkeeper Clayton Ince and Tomlin was on the spot to force the rebound over the line.
Seven minutes later it took a smart save by Ince to keep out a header from Warne and Yeovil continued to dominate the first half.
It was a different story after the break. Walsall had the rain and wind at their backs and within a minute Yeovil knew they would have some defending to do.
Michael Ricketts, who has one England cap in what seems the distance past, has joined Walsall from Oldham Athletic and he buzzed through the home defence with only Begovic to beat.
The keeper, who is on a three-month loan from Portsmouth, spread himself to make a brilliant save.
Walsall continued to apply pressure but the handling of Begovic was usually immaculate, although on one occasion when he failed to cut out a corner on 61 minutes he needed a goalline clearance from colleague Aidan Downes to keep Yeovil in front.