The visitors, under new manager Bruno Lage, dominated the second half but could not match the exquisite finish by Vardy four minutes before half-time.
Vardy had been getting in behind the Wolves backline even before his brilliant goal.
He had a left-footed shot saved by Jose Sa in the 10th minute after Ayoze Perez's lofted pass into the left channel.
Then, after netting when clearly offside five minutes later, Leicester's 2020/21 top scorer tried a bold backheel after James Maddison's angled ball over the top.
Wolves, with Raul Jimenez leading the line intelligently on his first league appearance since fracturing his skull nine months ago, looked dangerous on the counter-attack, mainly through Adama Traore.
Five minutes before Leciester's goal, Joao Moutinho won possession in midfield and played a perfectly paced pass through the middle. Traore sprinted clear and set himself to sidefoot goalwards but shot just past the post.
Vardy made Wolves pay in style. Ricardo Pereira muscled his way past two men down the right wing and pulled a low cross to the near corner of the six-yard area where Vardy ran in front of Conor Coady to flick a brilliant left-footed shot past Sa.
The former England man celebrated in customary style in front of the Wolves fans.
Youri Tielemans almost doubled the lead with a 20-yard shot in stoppage time but Sa parried.
The second half became a more open and entertaining affair as Leicester initially allowed Wolves to come onto them more.
Francisco Trincao regained the ball high up the field. The winger, on his Premier League debut after joining on loan from Barcelona, played a one-two with Ruben Neves and then saw his shot from close range deflected over the crossbar.
Leicester responded to Wolves' threat of dominance by switching to a 3-5-2 shape and a rare Coady slip allowed Vardy to send in Harvey Barnes but the England squad defender made a saving tackle.
Boubakary Soumare, the £17 million signing from Lille, and £15million defender Jannik Vestergaard, who joined on the eve of the game from Southampton, both came on to stiffen up Leicester's side.
The game was opening up thrillingly and Tielemans sent Barnes in on goal down the right hand side but Max Kilman anticipated his turn inside and averted the danger.
Wolves dominated the final stages but neither Kilman, dribbling in on goal, Leander Dendoncker, with a clear header, nor Morgan Gibbs-White, fed by Traore, could convert.