Brown Ideye gave the Baggies the lead before goals from James Morrison, Ideye's second and Saido Berahino handed Tony Pulis' men a passage into the last eight of the competition.
It was an afternoon to forget for West Ham, who were reduced to ten men when Morgan Amalfitano was involved in an altercation with his former West Brom team mate Chris Brunt.
Sam Allardyce must now pick his side up, with a big London derby against Tottenham Hotspur next weekend - and the trip to White Hart Lane is bound to be a tough one given the form Mauricio Pochettino's side are in.
Goalkeeper Adrian was left exposed against West Brom, but told the club's official website that the Hammers need to put things right against Spurs.
"We need to forget this horrible game because we have a tough one against Tottenham next week," said Adrian. "We need the next game to come quickly to help us get over this one, and we have a good opportunity to show a good level."
The two sides have already met once this season, and it finished 1-0 to Tottenham on the opening day of the season, with Eric Dier notching a last-gap winner for Spurs.
It will be a tough test for West Ham, but Adrian seems determined to bounce back in what will be a big game for the fans.