They won both matches between the sides last season and first-half goals by Lloyd Owusu and summer signing Paul Warne made sure they completed the hat-trick.
The visitors looked the sharper early on and it was no surprise when they took a 15th minute lead.
A cross by former Brighton defender Nathan Jones was back-heeled by Warne into the path of Owusu who calmly tucked away his fifth goal of the campaign.
Brighton should have equalised midway through the first half when a cross from Andrew Whing was headed down by Bas Savage into the path of Dean Hammond but the skipper skewed wide from 10 yards.
Yeovil made the most of that let-off by doubling their advantage three minutes before the break.
Marcus Stewart challenged for possession in midfield with Hammond and the ball broke kindly into the path of Owusu.
He crossed for Warne to add to his goal against Brighton last season - when he was with Oldham - with a crisp half-volley.
It could have been even worse for Brighton by half-time. Owusu, a real handful for the home defence, robbed George O'Callaghan and powered between central defenders Guy Butters and Tommy Elphick but ruined his good work by shooting straight at goalkeeper Michels Kuipers.
Brighton improved in the second half once Jake Robinson and Alex Revell had been brought on.
They reduced the arrears on the hour when Revell was brought down just outside the box and the resulting free-kick from Dean Cox was blocked by Warne with a raised arm as he broke from the end of the wall.
Hammond converted the penalty and Brighton spent the rest of the match trying to force an equaliser.
Robinson went close with a header but Yeovil were always dangerous on the break and Owusu almost put the issue beyond doubt with a toe poke which Kuipers turned away for a corner.