Williams, normally a left-back, has been handed a midfield slot because of injuries and he has responded with a series of impressive performances under Barnsley boss Andy Ritchie.
And when defender Neil Austin was brought down by Yeovil's ex-Huddersfield man Efetobore Sodje, it was Williams who grabbed the ball, determined to take the penalty.
The left-footed 21-year-old became the hero as he sent Yeovil keeper Chris Weale the wrong way with a smart spot-kick.
The game was long on endeavour and work-rate, but extremely short on skill.
Barnsley did start brightly and two-goal top scorer Paul Hayes almost made the breakthrough in the opening minutes but found Weale in top form.
Yeovil handed a league debut to their Argentine signing Pablo Bastianini and he worried the Barnsley defence throughout.
He almost netted with an audacious 35-yard lob that home keeper Nick Colgan did well to deal with on his line.
Yeovil went close to breaking through in the 44th minute when Darren Way's 25-yard thunderbolt beat Colgan but cannoned back off the Barnsley bar.
Yeovil had the better of the early second half exchanges and Bastianini twice had goal bound shots stopped before the Argentine went down in the box claiming a penalty, only for referee Ian Williamson to wave play on.
Barnsley gradually fought back and Aussie midfielder Jacob Burns hit the post with a fine 20-yarder before Williams popped up with the winning penalty.