However, the Baggies needed a penalty shootout to squeak through
West Brom have reached the fifth round of the FA Cup, but they went all the way to penalties before winning at League One team Peterborough.
The teams were 1-1 after 90 minutes and following extra-time, before the Premier League side beat the League One team 4-3 in the spot-kicks competition.
They will go to Reading next.
Former St Patrick's Athletic player Chris Forrester earned plenty of praise - including pre-game - for his performance in a Peterborough side which took the lead through Jon Taylor in the second half.
"He's been compared to Michael Carrick by the owners and by Graham Westley himself. It's about building up the profile of the players. He's stepped in from League of Ireland. He's another one that could potentially be pushing on for the Ireland squad over the next few years," said Kevin Kilbane while on punditry duty with BBC.
However, ex-Manchester United midfielder Darren Fletcher equalised within the 90 minutes to force extra time with a half-volley from the edge of the box.