A James Hayter brace and an own goal from Tony Craig on his home debut sealed a deserved win for Gary Johnson's side.
Brentford looked toothless in front of goal, but Clayton Donaldson's curled 55th-minute equaliser gave them hope after a lacklustre first half.
Bees debutant Paul Hayes missed a golden chance to give his new side the lead with his first ever touch after Yeovil's Byron Webster had handled in the box, but his low spot kick was easily saved by visiting goalkeeper Marek Stech and that was the platform for the West Country side to hammer home their superiority.
Hayter, who had broken the deadlock with a smart volley after Craig's defensive blunder, added to his tally in the 80th minute when he waltzed through the home defence to rifle home.
And Uwe Rosler's misery was compounded when new left-back Scott Barron was beaten for pace by Lewis Young, whose cross was smashed into the roof of the net by a backtracking Craig.