In a near repeat of Tuesday's Premier League game between the sides, which Villa won 2-1, Fabian Delph and Scott Sinclair struck to take Tim Sherwood's team into the last four for the first time since 2010.
Both teams finished the game with 10 men, with Claudio Yacob sent off for West Brom and Max Grealish dismissed for Villa, while play had to be temporarily suspended late on when a number of home fans poured onto the pitch.
But Villa manager Sherwood said: "I don't think it's scary. It probably is for a West Brom player. Emotions are running very high after two wins and it's been a huge week for the football club."
Giant-killers Bradford City had earlier been taken to a replay by Reading. Liverpool host Blackburn Rovers on Sunday and holders Arsenal travel to Manchester United in the tie of the round on Monday.
Also Read
But neither player was present for the reunion, with Boaz Myhill replacing Foster in the West Brom goal and a hip injury obliging Benteke to cede his place to Sinclair.
Pulis led Stoke City to the final in 2011 and his current charges made an enterprising start, with Saido Berahino working Shay Given before Brown Ideye somehow contrived to lift Craig Gardner's inviting cross over the bar.
But it was Villa who drew first blood in the 51st minute when Delph collected a pass from Charles N'Zogbia and bludgeoned a low shot inside Myhill's near post.