Albion have a crucial lead at the Bet 365 Stadium.
Jose Izquierdo put the Seagulls in front on 32 minutes.
Izquierdo had an earlier chance which just flew over.
At the other end Badou Ndiaye has gone close for Stoke as has Xherdan Shaqiri.
Albion look sharp on the counter attack and will have to look sharp overall in the second half.