The Seagulls ran riot to close the gap between the teams towards the bottom of the table to three points with a game in hand.
To make matters worse for Yeovil, they finished the game with striker Paul Warne in goal after Josh Wagenaar had been sent off and all three substitutes had already been used.
The rout began in the 16th minute when Jason Jarrett threaded a pass inside Craig Alcock for Dean Cox to fire home a right-foot drive from inside the box.
The pint-sized winger's first league goal since November was followed by a 14th of the season for skipper Nicky Forster in the 29th minute.
Forster, back in the starting line-up after a calf injury, latched on to a clever back heel from Cox to beat Wagenaar with a low drive from 12 yards.
Yeovil improved in the early stages of the second half but the match was over as a contest when Forster added his second and Brighton's third in the 62nd minute.
He picked up a pass from Cox through the middle and ghosted away from Alcock to score with an angled left-foot shot.
Forster was substituted shortly after to a standing ovation to allow Glenn Murray to make his first appearance since January following hernia surgery.
Wagenaar protested about the spot-kick and that proved costly in the 83rd minute when he scythed down substitute Craig Davies just outside the area to receive a second card.
Murray converted an 80th minute penalty after Cox's cross had been handled by Terry Skiverton, the Yeovil manager and centre-half.
Warne could not prevent Cox completing Yeovil's misery a minute from time with a low drive from Davies' pass.