Horwood crashed home the winner just three minutes from time with a fearsome half-volley, which bounced in off the underside of the crossbar.
Horwood’s heroics capped a fine comeback by in-form Pools after Nolberto Solano’s free-kick had cancelled out Steven Gregory’s excellent opener for Bournemouth.
Gregory gave the Cherries the lead eight minutes before half-time in emphatic style, rifling the ball past visiting goalkeeper Scott Flinders from 25 yards.
Solano equalised in the 42nd minute with his second in as many matches, but it was scarcely deserved as Bournemouth had dominated the opening half.
Flinders saved well from Harry Arter after only three minutes before Marc Pugh dragged a shot wide 18 minutes later, while the visitors’ best effort before Solano’s equaliser was Anthony Sweeney’s miscued shot after the ball had fallen luckily into his path.