Record signing Ahmed Musa scored his first goal for the club, while Shinji Okazaki and Christian Fuchs struck after the break – the latter’s effort a superb volley – to secure a convincing win.
Yohan Cabaye scored a consolation for the Londoners and Palace pressurised the hosts in the final five minutes as they attempted an unlikely comeback.
But it was too late against a Leicester side who showed something of the form that won them the title last season, even without England striker Jamie Vardy in the starting line-up.
Vardy, who played in the 1-0 win over Copenhagen and has not scored in eight games, was rested with manager Claudio Ranieri saying he needed to rotate his players as they juggles European and league commitments.
The Italian’s decision was justified as Okazaki added guile to the Leicester attack, while Islam Slimani was a menacing presence up front.