Leicester got the opener their play deserved when Alex McCarthy spilled Riyad Mahrez’s 25-yard shot straight at the feet of the lurking Vardy who was in no mood to waste the final-day present.
Leicester doubled their lead two minutes before the break. Schlupp’s cross from the left evaded everyone until fellow wideman Albrighton arrived to crash home.
Austin tested Schmeichel from distance on the restart, before Irish teenager Reece Grego-Cox fluffed a big chance of a debut goal.
The visitors were punished when Ulloa deflected home Wes Morgan’s shot before Richard Dunne headed Albrighton’s cross straight to Cambiasso, and Leicester’s player of the year delivered a fine finish low past McCarthy.
There was some consolation for Rangers when Austin met Barton’s free-kick but the striker’s 18th Premier League goal of the season is likely to be his last for the club as others will compete for his signature in the summer.
Leicester had the last word four minutes from time when a loose ball ran to Kramaric and the Croatian made no mistake with an unerring finish.
Schmeichel,Wasilewski (De Laet 46), Huth, Morgan, Albrighton, Cambiasso (Drinkwater 76), King, Schlupp, Mahrez, Ulloa, Vardy (Kramaric 65).
McCarthy, Onuoha, Dunne, Hill, Yun (Kpekawa 85), Phillips, Henry (Comley 80), Barton, Fer, Austin, Grego-Cox
Michael Oliver (Northumberland).