Albion trail Spurs at Wembley after Serge Aurier whipped in a goal five minutes before half time.
His shot – taken under pressure – looked suspiciously like a cross.
Spurs have had most of the play with Albion’s best chance cowing from a header from Shane Duffy.
It is Albion’s first visit to Wembley since Sunday 2 June 1991 when Notts County beat Brighton 3-1 in the play-off final for a place in the top flight.