The former England striker had been starved of service until clinically finishing a brilliant Leicester counter early in the second half, which ultimately proved enough to clinch a first win at Stamford Bridge since 2000.
It was a hugely frustrating afternoon for Maurizio Sarri's side, which controlled large periods of the game and saw Eden Hazard — one shy of 100 competitive goals for the Blues — hit the crossbar in the first half as well as Marcos Alonso strike the post in the 91st minute when clean through.
Chelsea, which lost a league match at home for the first time under Sarri, consequently head into Christmas 11 points behind leader Liverpool, while rumours that Leicester was planning on sacking Claude Puel may subside after this much-needed win.
Chelsea's play was sharp if lacking in incisiveness early doors, although David Luiz was desperately close to meeting Pedro's flick on from a Willian corner.
The visitors had an almighty let-off when Hazard pounced on Harry Maguire's poor control and rifled an effort against the crossbar.
Neither team had a shot on target until the 41st minute with Kepa Arrizabalaga's strong hand keeping out Wilfred Ndidi's stinging 30-yard drive.
Willian tamely struck at Kasper Schmeichel after a fine team move, while Jorginho's well-hit half-volley forced the Leicester keeper into action again as Chelsea finished the half strong.
The Blues were caught cold six minutes after the break, though. Leicester launched a counter-attack that led to James Maddison slipping in Vardy to emphatically fire past Kepa when one-on-one.
Schmeichel was sharp to keep out Hazard's left-foot effort from a tight angle, and at the other end Kepa's spill from Marc Albrighton's cross needed swift action from Cesar Azpilicueta to deny Vardy.
Leicester's goal lived a charmed life in the closing stages with Antonio Rudiger heading wide from point-blank range and Alonso fluffing his lines by striking the left post when one-on-one.
The festive season kicks into gear with Chelsea making the hop across London aiming to bounce back at Watford on Boxing Day (27 December AEDT), while the Foxes will look for another unlikely win at home to Manchester City.