Brighton had taken the lead on 19 minutes when Yeovil defender Scott Guyett failed to clear the ball, losing out to Nicky Forster. The Brighton top scorer slipped the ball to Alex Revell who had the comparatively simple task of beating Steve Mildenhall.
Yeovil hit back in determined fashion but Brighton defended in numbers and it was not until the 42nd minute that the equaliser arrived.
It was a touch of class and ex-Premiership man Marcus Stewart provided it.
He slipped a delightful pass between two defenders and Gary Dempsey, a summer signing from Aberdeen, crashed home his first goal for the Somerset club.
The winner came five minutes into the second half. Zoltan Stieber, a young left winger on loan from Aston Villa got in a telling cross which caused consternation in the Brighton defence.
The ball ballooned into the air off the head of Joel Lynch and the ball fell kindly for Stieber who knocked it into an empty net.
The youngster could have had another on 75 minutes when he fired into the side netting and Lloyd Owusu, on as a substitute, also went close in the closing stages.