The goal came in the 59th minute after Villa defender Pau Torres made a sloppy defensive play.
Dwight McNeil got a shot off that Emiliano Martinez saved, but Thierno Barry managed the rebound, chipping it over the Argentine goalkeeper.
Victor Nilsson Lindelöf remained on the bench throughout the match.
Luckily for third-placed Villa, they weren't the only team at the top to drop points this round. First-placed Arsenal cruised past Nottingham Forest, shaky Manchester City lost the derby to Manchester United, and fourth-placed Liverpool drew with Burnley.
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