New signing Carles Gil curled home a stunning strike in the 51st minute before Andreas Weimann sealed the victory with his neat finish 20 minutes later.
Callum Wilson did get an equaliser for the Championship side in injury time but it wasn't enough to stop the Cherries slipping to defeat.
Goals for Aston Villa have been limited this term and they have only scored twice in one game three times this season.
Villa haven't scored a Premier League goal since December after their 1-1 draw with Manchester United.
To make Villa's day even better, Fabian Delph has agreed a new deal with the club.
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