West Brom booked their place in the FA Cup fourth round with a routine 1-0 replay win at Bristol City on Tuesday.
Championship strugglers City were left to rue missed chances by Wes Burns, Luke Freeman and Aaron Wilbraham, with Salomon Rondon scoring the game's only goal shortly after half-time, converting a cross from Craig Dawson with a classy touch and finish.
Premier League outfit West Brom had not won away since October but closed the match out easily to book a home fourth-round tie with League One side Peterborough United.
West Brom boss Tony Pulis selected the fit-again Ben Foster in goal and left striker Saido Berahino out of his squad amid continued rumours of a January exit, while James Morrison and Darren Fletcher missed out through injury.
City's Freeman had the game's clear first sight of goal on 10 minutes, but he cut inside and struck his shot straight at Foster, who continued his rehabilitation from a serious knee injury with another 90 minutes.
Burns then had a golden chance to put City in the lead. Bobby Reid slipped the ball in behind Chris Brunt and Burns ran through on goal only to pull his shot wide of Foster's far post.
Craig Gardner cushioned a 20-yard half-volley narrowly wide on 29 minutes but the hosts, full of confidence after beating Championship leaders Middlesbrough 1-0 on Saturday, were on top.
Stephane Sessegnon, James McClean and Rondon all saw efforts from long distance fly well off target, but Pulis' side almost took the lead on 40 minutes.
City could only clear a cross to Gardner, whose volley bounced kindly for Gareth McAuley, who headed over from just a few yards out.
That miss was almost punished on the stroke of half-time, but Freeman curled a free-kick narrowly wide after Reid had been bundled over on the edge of the box by Claudio Yacob.
West Brom took the lead on 52 minutes. Dawson lifted a cross over Aden Flint's head and Rondon chested the ball down before prodding it beyond 19-year-old goalkeeper Max O'Leary, who was making his full debut for City.
Wilbraham could have levelled the scores just before the hour-mark but he headed Burns' precise centre over the crossbar from close range.
Foster saved from Burns after the returning goalkeeper flapped at a cross on 81 minutes, before Nathan Baker headed Marlon Pack's free-kick well wide.
West Brom had won their past three FA Cup ties against lower-league opposition and made it four in a row by shutting City out despite late pressure.