Vardy superbly converted Riyad Mahrez' pass after a Brede Hangeland mistake on the hour-mark at the King Power Stadium as he became only the eight player - alongside the likes of Thierry Henry and Alan Shearer - to score in seven successive Premier League games.
Leicester are now level on points with Manchester United, albeit having played a game more.
Prior to the goal, he was quiet, but played with a rippling confidence after it, although he never had any other good chances to add to his tally.
Both teams adopted an attacking outlook in the opening stages but the game soon settled into the pattern of Leicester pressing hard when out of possession and playing a cautious style when they had the ball.
The match was one of few chances, with Marc Albrighton's shot which hit the post early in the first half the next best chance of note.
Palace felt they should have had a penalty when substitute Wilfried Zaha went to ground in the box under the challenge of Christian Fuchs but Kasper Schmeichel was not a busy man as Leicester secured their first clean sheet of the season.
The victory came through another moment of magic from Vardy, whose reputation continues to grow with every game.
