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.
Source: PA
Source: PA