The hosts started brightest and had their first chance after five minutes. Jose Izquierdo sent in an early cross from the left, but Glenn Murray couldn’t sort out his feet and failed to connect from eight yards out.
Stoke then pushed for the opener and Ryan Shawcross rose highest to meet a corner at the back post, but his header was tipped over the top by Mat Ryan in the Brighton goal.
Izquierdo then saw an effort whistle past the post but just as the hosts really started to threaten, they fell behind to a well-taken goal from Maxim Choupo-Moting. Xherdan Shaqiri played a long ball over the top for the striker to run onto, which he controlled expertly before calmly slotting past Ryan.
Brighton responded well and equalised on 44 minutes following stern work in the midfield from Davy Propper. He danced his way from the middle of the park to the right flank before cutting back to Pascal Gross, who made no mistake and tucked in at the near post.
However, they were level for little more than a minute. Choupo-Moting met a corner at the back post and Kurt Zouma came in to nod home from three yards out and ensure Stoke took a lead into half-time.
The hosts didn’t give up though and quickly drew level again after the restart. Murray's disguised pass slipped in Izquierdo on the left byline and his first shot was blocked, but he sent the second attempt past Lee Grant into the far corner.
This time, Brighton composed themselves and weathered the subsequent storm thrown at them by Stoke. Shaqiri came close to putting Stoke ahead for a third time with 20 minutes to play, but his fierce left-footed drive flashed just past the far post.
The remaining minutes of the game lacked the pace and power of the first half, with neither side looking like scoring the winner.
A draw was probably the fair result, but Brighton will be happier given the fact they came from behind twice to secure a point.