Maurizio Sarri's side paid the price for failing to convert their chances when Vardy netted early in the second half to hand the Blues their first defeat in five games.
Chelsea's disjointed display surrendered an 18-match unbeaten run at the Bridge dating back to Tottenham's victory in April.
Sarri has insisted he does not expect Chelsea to challenge for the title this season, the Italian rating Liverpool and Manchester City as "two steps ahead" of the Blues.
This was further evidence to support Sarri's concerns, with Chelsea left trailing 11 points behind leaders Liverpool.
Chelsea remain in fourth place in the Premier League, but they are now above fifth-placed Arsenal only on goal difference, leaving them facing a tense bid to qualify for the Champions League in the second half of the season.
Leicester's first win at Chelsea since September 2000 was well-timed for Foxes boss Claude Puel, who has endured recent reports he could be sacked just 14 months after he arrived from Southampton.
Chelsea almost took the lead in bizarre fashion after just two minutes when David Luiz launched a long ball towards Willian.
Luiz's pass bounced on the edge of the Leicester area, prompting Foxes keeper Kasper Schmeichel to rush off his line, but when neither he or Willian could make contact, the ball bounced just wide of the empty net.
Pedro was inches away from putting Chelsea in front when he met Willian's corner with a glancing header that flashed wide as Luiz stretched in vain to turn it in.
But despite their territorial dominance, Chelsea's passing and movement wasn't precise or fast enough to prise Leicester open.
Significantly, Hazard was again deployed up front as Sarri continued with the experiment of using the Belgian playmaker as a 'false nine'.
Hazard has been less than effusive in his thoughts about the role so far, dropping hints that he would prefer to return to his usual wide position.
He remains by far Chelsea's most dangerous player wherever he lines up, but there is little doubt his best performances come on the flanks.
Hazard had been the midweek League Cup match-winner against Bournemouth and he should have bagged his 100th Chelsea goal after pouncing on a slip from Leicester's Harry Maguire for a fierce close-range shot that cannoned off the bar.
It was a crucial moment.
Ndidi's thunderous long-range drive forced Kepa Arrizabalaga to make a fine save before Jorginho produced a powerful effort of his own that Schmeichel punched away.
Not for the first time this season, Chelsea's miscues in attack proved fatal.
Showing the cutting edge that Sarri's team lacked, Leicester punished a moment's loss of concentration to snatch the lead in the 51st minute.
James Maddison slipped a perfect pass to Vardy, who escaped Cesar Azpilicueta before burying a cool finish past Kepa for his sixth goal of the season.
It was the first time Chelsea had conceded a goal at home in six matches and inevitably they turned to Hazard for inspiration.
Beating Leicester's offside trap, Hazard cut in from the left for a stinging strike that Schmeichel blocked at his near post.
Sarri responded by sending on Olivier Giroud and Ruben Loftus-Cheek, allowing Hazard to return to the left wing.
But Leicester were defending superbly and Chelsea's luck was out in stoppage-time when Marcos Alonso's shot hit a post and rolled along the goalline to safety.