Robin van Persie scored his first goal in over a month to break the deadlock, sprinting onto a long ball over the top to volley past Mark Schwarzer amid suspicions of offside before Radamel Falcao bundled in a second five minutes later.
The game was as good as over just before half-time when Leicester defender Wes Morgan lost his footing and diverted Daley Blind's header past Schwarzer.
Marcin Wasilewski added a late consolation when he headed home Marc Albrighton's cross just over 10 minutes from time.
