The visitors controlled much of the early play, and pushed particularly hard in the 16th minute when Alex Frutos crossed low for Dean Hammond, but his run was slightly too eager and he crashed into the brave Steve Simonsen.
Frutos proved to be a thorn in City's side with several first-half free-kicks being whipped in viciously to keep Simonsen on his toes.
His best effort arrived in the 20th minute from open play, when he stuck a thunderous 25-yard volley that the goalkeeper found too hot to handle, resulting in him conceding a corner.
The Potters broke the deadlock in the 35th minute when Paul Gallagher's incisive pass between allowed Sam Bangoura a shot which he took confidently, placing it underneath Alan Blayney.
Things became slightly more heated before the break when a foul on Seb Carole caused Mark McGhee to storm to the touchline, but a showdown with City skipper Michael Duberry soon calmed the Scot.
Gallagher continued to get closer to a goal and four minutes later his quick free-kick beat Blayney but not his crossbar, bouncing out to give Brighton the chance to clear.
Stoke added a second in the 68th minute when the Seagulls failed to clear a Lewis Buxton cross, giving Mamady Sidibe the chance to shoot from close-range - but it was Darel Russell's follow up that bagged the goal.
The Potters finished the job in the 75th minute with contract rebel John Halls providing a pinpoint cross for Bangoura, whose header found the bottom left corner of Blayney's net.