Although League One Leyton Orient saw plenty of the ball, a strike by Stuart Nicholson just before the break and two superb second-half efforts from Darren Carter and Jonathan Greening ensured there was no chance of a shock.
Both sides made six changes to their weekend line-ups, but it was Orient who were quickest out of the blocks and carved out the first chance when Donny Barnard's header was deflected away following a Wayne Corden corner.
However, West Brom always looked dangerous on the break and O's keeper Glyn Garner was forced to make a smart stop from Ronnie Wallwork.
As the half progressed Orient almost went ahead when striker Jabo Ibehre latched onto a poor clearance from keeper Pascal Zuberbuhler, but his snapshot flew inches wide.
As Orient continued to press Zuberbuhler atoned when he saved Clayton Fortune's header, following Matthew Lockwood's right wing corner.
West Brom debutant Kevin Phillips was a constant menace and saw a shot deflected over before the visitors struck on 41 minutes.
Richard Chaplow led a lightening break and when Garner parried his fierce drive Nicholson swept the rebound home.
After the break Orient had their chances to get back into the game but Corden wasted a glorious chance when Zuberbuhler saved his close-range effort following neat play.
Craig Easton then saw an effort punched over the bar before West Brom stepped on the gas and struck twice to finish the game as a contest.
The warning signs were there when Nicholson sent a header just wide, but there was to be no escape for the hosts when, on 71 minutes, Carter volleyed home superbly from the left following Greening's excellent cross.
Five minutes later the visitors struck a third when Greening played a marvellous interchange with Nicholson and then fired low beyond Garner's desperate dive.
Orient tried to respond and sub Gary Alexander went close with a couple of efforts but it was too little too late to halt West Brom's march into the next round.