Mauricio Pellegrino's charges went on to double their lead just before the hour through Dusan Tadic, who allowed Guido Carrillo's probing ball to bounce before lashing a chip into the back of the net.
Salomon Rondon's impressive volley from Grzegorz Krychowiak's delivery shortly after Southampton's second restored West Brom's hopes of progression and Ahmed Hegazi came close to an equaliser soon after, only for Southampton to clear his effort off the line.
Alan Pardew's charges could not force an equaliser come the final whistle despite their second wind and finished a testing week by exiting the world's oldest cup competition.
WEST BROMWICH ALBION (4-4-2): Foster; Dawson, McAuley, Hegazi, Evans; Phillips (Burke 89'), Krychowiak (Field 82'), Barry (Brunt 72'), McClean; Rodriguez, Rondon
SOUTHAMPTON (4-2-3-1): McCarthy; Soares, Hoedt, Stephens, Bertrand; Hojbjerg (Romeu 78'), Lemina; Ward-Prowse, Tadic, Redmond (Gabbiadini 72'); Carrillo (Sims 85')