Vardy made no mistake with his first spot kick on 15 minutes after Wolves were penalised for handball when Dennis Praet's cross hit Max Kilman's hand, the 33-year-old England international sending keeper Rui Patricio the wrong way.
Marc Albrighton replaced Luke Thomas for Leicester at the break and almost made an immediate impact, but Youri Tielemans headed his ball into the box just wide. He also wasted another good chance as he blazed a shot over the bar.
Wolves swarmed forward looking for an equaliser and goalkeeper Kasper Schmeichel pulled off a stunning save to deny a Ruben Neves shot from the edge of the box, diving high to his left to keep the ball out.
"That's what you work on as a keeper, it's what I'm there for. The whole team defended brilliantly all game -- they had one or two chances and that was it," Schmeichel told Sky Sports.
Leicester could have doubled their lead on 82 minutes but Harvey Barnes blazed a deflected strike over the bar. From the resulting corner Christian Fuchs hit a powerful shot that might have troubled the keeper had it not struck team mate Jonny Evans.