A second-half goal from Nwankwo Kanu has sent Portsmouth through to their first FA Cup final in 69 years.
The match sparked into life when Kanu put Pompey in front of West Brom in the 54th minute.
Former Baggies striker Kanu kicked in the ball after keeper Dean Kiely stopped Milan Baros but defender Zoltan Gera failed to clear it.
Portsmouth will face the winners of the all-Championship tie between Barnsley and Cardiff on Sunday on 17 May.
The Cup final will see Portsmouth boss Harry Redknapp going for his first major honour as a manager.