Albert Adomah scored twice to end Barnet's run of 13 games without a win and ensure departing manager Paul Fairclough bowed out on a high.
Bournemouth fell behind when Adomah latched onto a clearance and turned two defenders before beating Shwan Jalal.
Danny Hollands then hit the bar for the Cherries with a half-volley.
After the break Alan Connell was denied on the line by Ismail Yakubu and minutes later Adomah rounded Jalal to wrap up victory for Barnet.
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Booked: Jalal.
Goals: Adomah 24, 70.
Att: 4,725
Ref: Fred Graham (Essex).
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