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 and Pedro, who had a brace, were the other scorers for Chelsea.
The win lifts Chelsea to ninth in the league table, while Aston Villa remain rooted to the bottom.
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