Darren Fletcher nearly opened the scoring in the eighth minute at Falmer Stadium with a shot inside the box following a scramble but Lewis Dunk cleared the strike on the goal-line for the Seagulls.
The Potters threatened after 20 minutes and had a sustained pressure at opposition half with Xherdan Shaqiri the main threat.
Eric Choupo-Moting punished Chris Hughton's charges for sloppy defending, side-footing a right-footed strike from inside the box into the bottom corner following a sublime pass from Shaqiri.
Glenn Murray was seemingly brought down by Ryan Shawcross with a sliding tackle inside the box but surprisingly the referee did not heed the calls from the home fans to award a penalty.
The hosts deservedly levelled matters a minute before halftime through Pascal Grob's first-time finish against the run of play.
However, Hughton's troops let it slip in first-half stoppage time as Kurt Zouma powered home a header to restore the lead for the visitors.
The hosts started the second half strongly, attacking mainly through the wings.
Jose Izquierdo restored parity for the Seagulls on the hour mark with a close-range finish after a clever pass from Murray.
Shaqiri came close to handing Hughes' troops the lead in the 71st minute but his left-footed effort missed the target by inches.
The match slowed down somewhat after 80 minutes as both sides were beginning to be cautious in their approach.
The final 10 minutes were tense with the hosts particularly adventurous while the Potters played on the counter-attack but ultimately it ended all square in an entertaining match.