The visitors were undone by three first-half headers, with John Carew netting after 14 minutes and his strike partner Jon Walters making it 2-0 eight minutes later.
Walters then set up Potters captain Ryan Shawcross just before the interval, and although Brighton improved in the second period, they were unable to reduce the deficit.
It seemed Tony Pulis' team might have a considerable threat to contain with the npower League One leaders going into the game having scored eight times in their previous two matches.
As it turned out, though, the Barclays Premier League side were rarely troubled and - certainly in the opening 45 minutes - did most of the attacking themselves.
Rory Delap caused the visitors problems with his long throws in the early exchanges, Seagulls goalkeeper Peter Brezovan fisting one on to Agustin Battipiedi's head and giving away a corner which Jermaine Pennant scuffed as he slipped over.
A Delap delivery yielded another corner soon after and the 34-year-old almost met it at the back post when it was swung in by Matthew Etherington.
It came as little surprise, then, that it was Delap's throw that led to Stoke's opener just before the quarter-hour mark.
The towering figure of Carew was there to flick it towards goal and the glove of Brezovan was not enough to stop the ball going in.
The hosts were already looking well and truly in charge and after Pennant headed Danny Pugh's cross wide and Walters struck a low drive into Brezovan's arms, they extended their advantage.
Marc Wilson crossed and Walters arrived at the near post to net his third goal of the competition this season by nodding the ball across Brezovan.
Stoke continued to press and Walters headed Pennant's pass off-target from a good position, with his protests that he had been impeded waved away by referee Howard Webb.
Pennant then laid the ball to Delap, who blasted high and wide from outside the box.
Etherington, who had missed last week's defeat at Birmingham with a hamstring problem and appeared to be in some discomfort, was substituted for Ricardo Fuller towards the end of the half, but the Potters' momentum did not let up.
Fuller won a corner in the 43rd minute after breaking into the box and from Pennant's delivery, Walters flicked the ball on for Shawcross to head home a third.
Brighton tried to get going after the restart, with Ashley Barnes sending in one shot that Thomas Sorensen dealt with and then a header which he could not apply any power to under the attention of two defenders.
Two minutes later Elliott Bennett fell in the box and claimed he had been fouled by Robert Huth, but play continued.
Brighton manager Gus Poyet made a double substitution, introducing Jake Forster-Caskey and Fran Sandaza for Battipiedi and Glenn Murray.
The Seagulls were fortunate not to find themselves further behind within moments, though, as Carew's pass went unconverted after he slipped the ball across a gaping goal.
The Norwegian was then brought off by Pulis, with Kenwyne Jones taking his place.
There was another moment of uncertainty for Brezovan as he caught Walters' cross, but only just managed to keep it from crossing the line.
Brighton - late as it was - were growing into the game, though, and after Cristian Baz had come on for Barnes, Sorensen dived at the feet of Sandaza to halt a slick move.
Baz then drew a save out the Danish stopper, but at the other end, Brezovan was called into action to block a fierce Fuller effort.
Forster-Caskey also tried his luck to no avail and Fuller sent a shot into the side-netting seconds before the final whistle.