Germany defender Rudiger bundled home Ben Chilwell’s deflected corner with his thigh as Chelsea shook off Timo Werner’s two disallowed goals at Stamford Bridge.
Jorginho calmly slotted a spot-kick to seal the Blues’ vital victory, with the only worry being an early enforced exit for key midfielder N’Golo Kante.
Kelechi Iheanacho sidefooted in for Leicester to set up a nervy finish, but Ayoze Perez missed a golden chance as Chelsea held out for a result of major significance.
The Blues avenged Saturday’s 1-0 FA Cup final defeat by Leicester with a pulsating showing in west London, to leapfrog the Foxes into third place in the Premier League table. Beat Aston Villa on the road on Sunday and the Blues will book the all-important Champions League qualification for next season.