The Foxes led at the half-hour mark through a Matt Doherty own goal, the defender heading in just as Wolves were on top at the King Power Stadium.
New signing James Maddison, who impressed in Leicester's opening defeat by Manchester United, curled in his first Premier League goal on the stroke of halftime.
The hosts were reduced to 10 men when Vardy, making his first start of the season, was shown a straight red for a high tackle on Doherty but Wolves were unable to capitalise.
Leicester manager Claude Puel lauded the Premier League newcomers and said his side were fortunate to escape with a win.
"Congratulations to them because they played well - they are difficult to read, they cause a lot of difficulty. It is difficult to defend against them," he said.
"We were lucky. My players kept a good attitude and mentality. It was important to have the right attitude."
Wolves' Portuguese manager Nuno Espirito Santo, who saw his side clinch a point in an opening-day 2-2 draw with Everton, was sanguine about the loss.
"The way we played makes me proud but I am not happy with the result. We have to be accurate in the final moment, we could and should do better," he said.
(Reporting by Christian Radnedge, editing by Ed Osmond)
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