Alexandre Pato scored on his debut as a seventh-straight league loss continued Aston Villa's slide towards relegation.
The home fans chanted against their players and owner Randy Lerner as the Blues took control in the second half.
Ruben Loftus-Cheek's deflected shot and Pato's precise penalty had given the visitors a healthy half-time lead.
Pedro scored twice - slotting in Oscar's pull-back and hammering home a loose ball - before Alan Hutton was sent off to compound Villa's misery.
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