Luke Nippard gave the Cherries an early lead and Ash Pope doubled the hosts’ advantage before the break.
Jack Hilton-Jones pulled one back late on but the Glovers couldn’t complete a deserved comeback despite dominating on the south coast.
Town began the contest on the front foot, but found themselves behind midway through the first period.
A good passage of play from Bournemouth created space for Nippard to convert against the run of play.
Prior to the interval, Alan Cornell’s side made it 2-0 as Pope netted from inside the area.
Yeovil upped their game in the second half and continuously pressurised the Bournemouth backline.
Very much in the ascendency, the young Green and Whites halved the eventual deficit.
The home side half-cleared a corner and Paulius Golubickas teed up Hilton-Jones who buried a first-time shot from 25 yards to set up a nervy finish.
The Under-18s battled hard for an equaliser, however a second score proved elusive.