Jamie Vardy struck first in the 11th minute with a header to the bottom right corner and Riyad Mahrez scored in the 18th and from the penalty spot in the 25th.
Former Chelsea coach Claudio Ranieri made a triumphant return to the league after 11 years away as Leicester continued its strong finish from last season when it managed to avoid relegation.
Jermain Defoe and Steven Fletcher grabbed second-half goals for Sunderland, while Marc Albrighton got Leicester's fourth at the King Power Stadium.
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