A curling free-kick from midfielder Richard Hughes condemned the Glovers to their first League One defeat of the campaign.
With Harry Redknapp, who has taken on an advisory role at Bournemouth, watching on from the stands, the Cherries dominated the first half.
They took a deserved lead after 35 minutes when Josh McQuoid was fouled by Yeovil stand-in skipper Byron Webster. Former Portsmouth midfielder Hughes took the resulting free-kick and fired a left-foot strike into the top corner from 20 yards.
Yeovil manager Gary Johnson made a double substitution before the break to try and spark his lacklustre team into life. However, it was Bournemouth who came close to doubling their lead moments before half-time when McQuoid's goal-bound strike was blocked by Richard Hinds.
The Cherries nearly extended their advantage in the second half but home goalkeeper Marek Stech thwarted Wes Fogden before Lewis Grabban and substitute Wes Thomas both shot wide.