Christian Benteke headed home Crystal Palace’s opener after being left unmarked in the box.
Wilfried Zaha then smashed home a second for the visitors before half-time.
Any chance of a Foxes fightback was ended on the hour mark after Vicente Iborra had a goal ruled out for a foul on James Tomkins.
And moments later Wilfred Ndidi was sent off after picking up a second yellow for diving in the box.
Bakary Sako made it three in stoppage time.
The win lifts Palace to 14th in the Premier League – three points from danger.
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