West Brom are into the FA Cup semifinals after their stunning 5-1 victory over Bristol Rovers.
Three upsets prior to this clash at the Memorial Stadium meant Portsmouth were the only top-flight side through to the last four, and helped by an Ishmael Miller hat-trick, Albion made sure there would not be a fourth shock.
Baggies striker Kevin Phillips accepts there is now a real chance for Albion to claim silverware and told BBC Sport: "It's been a bizarre weekend for the FA Cup and we knew we had a fantastic chance. We had to be professional tonight, keep it tight and take our chances and we did that, and what an opportunity now.
"We said to the players at the beginning that these opportunities do not come around very often and we have got to take the chances when we can. We will look forward to our day at Wembley and hopefully we can do the business there."
Miller added Albion's second and his first with a cracking turn and shot before the half-hour mark but Danny Coles quickly halved the deficit.
The key moment came when Miller, who was stood way beyond the last man in the Rovers defence, latched on to a wayward defensive header to tuck away his side's third and his second.
Substitute Phillips added a fourth and Miller completed his treble with a well-placed left-foot shot.