The Cherries dominated for long spells and Yeovil were only in the game for a brief period in the second half.
Steven Gregory set the pattern with an excellent goal for the Cherries after six minutes. He picked up the ball 25 yards out and was given time and space to blast past goalkeeper Rene Gilmartin's right hand.
The visitors doubled their lead after 26 minutes when Yeovil failed to cure a Marc Pugh corner and Wes Fogden was left unchallenged to score from close range.
Yeovil's Bondz N'Gala crashed a header against the bar just before half time but the visitors then reduced the arrears after 66 minutes when skipper Paul Huntington moved up from the back to head home Gavin Williams' right-wing corner.
However, Bournemouth deservedly had the last word when full-back Charlie Daniels embarked on a mazy dribble from the back and fired home from an angle, leaving defenders trailing in his wake.