The Seagulls took the lead in the sixth minute when a right-wing cross looped off the boot of Craig Alcock and fell kindly for Andrew Crofts, who blasted in a low drive from just inside the box.
Brighton were in the ascendancy and it was no surprise when they increased their lead in the 41st minute with Liam Dickinson taking advantage of hesitancy in the Yeovil defence to score.
However, as the first half went into stoppage-time, Scott Murray pulled a goal back for the Glovers with a superb strike across the goalkeeper as he cut in from the right.
Murray wiped the smiles off Brighton faces nine minutes from the end when the Somerset club were awarded a penalty after Jake Wright fouled Terrell Forbes.
The former Bristol City winger, making only his second Yeovil start, hammered his spot-kick into the roof of the net.