Salomon Rondon struck the decisive blow eight minutes into the second half to consign City to an FA Cup exit by a solitary goal at the hands of Premier League opposition for the second year running.
The Venezuelan international showed his scoring instinct to convert one of very few chances on a freezing night at Ashton Gate.
The interim management duo of John Pemberton and Wade Elliott were not afraid to mix things up, despite an impressive last-gasp win over Sky Bet Championship leaders Middlesbrough in their first game in charge.
The overhaul included five changes to the starting line-up and seven Academy graduates in the squad as a whole.
Nineteen-year-old goalkeeper Max O’Leary made the first start of his career in the absence of the cup-tied Richard O’Donnell and injured Frank Fielding, having come off the bench at half-time in the initial tie at The Hawthorns ten days ago.
There was also a first start of the season for Scott Wagstaff on the left wing, as well as recalls for Mark Little, Aaron Wilbraham and Luke Freeman, who missed the Boro victory with a dead leg.
Out went O’Donnell and the injured Korey Smith, with Luke Ayling, Joe Bryan and Jonathan Kodjia on a City bench that also included youngsters Jojo Wollacott, Zak Vyner and Joe Morrell.
Albion started with a sense of purpose as James McClean charged into the box, but the Irishman snatched at a shot from a rapidly diminishing angle when crying out for a low ball across the six-yard box.
But City would more than hold their own throughout a closely-fought first period, carrying on from where they left off in the second half in the West Midlands, and carved out the first notable chance after 14 minutes.
Fittingly, it involved the two outfield Academy starters in the starting XI. Bobby Reid found a pocket of space after some neat interplay in midfield and slid an excellent pass in behind the defence for Wes Burns, who had a clear sight of goal but dragged his shot wide with only Ben Foster to beat.
West Brom lost the services of set-piece specialist Chris Brunt soon after – something that may have calmed the nerves of O’Leary, not that the rookie had been kept particularly busy.
Albion seemed to have a plan to test out the youngster, but were having problems hitting the target.
Stephane Sessegnon, Craig Gardner, Rondon, Victor Anichebe and McClean all tried to work O’Leary from distance without success, leaving the City fans behind the goal feeling more in danger than their wide-eyed custodian.
City’s only opportunity so far remained the only clear sight of goal for either team until the visitors threatened to inflict a sense of deja-vu on the Championship side four minutes before the interval.
In a repeat of the set-piece that forced the replay, West Brom played a wide free kick short rather than sending it directly into the box.
This time the ensuing cross was met by a City head only as far as Gardner, whose volley into the ground bounced up invitingly for Gareth McAuley, but the veteran defender sent the chance up over the bar rather than down into the net.
City then forced a free kick of their own in first-half stoppage time, right on the edge of the Albion box after Reid was brought down by the niggly Claudio Yacob, as Freeman’s shot from the dead ball left Foster rooted and sailed only inches wide.
The hosts had every reason to believe an upset remained on the cards, but would find themselves having to do it the hard way as Rondon struck the opener eight minutes after the break.
The Baggies’ club-record signing showed some clever movement to peel away between two City defenders and an assured touch to take Craig Dawson’s cross on his chest before tucking the ball underneath O’Leary from no more than six yards.
From that point on, chances would prove few and far between until the closing stages.
West Brom, though far from spectacular, were not short of know-how in nullifying much of City’s attacking threat.
But the home team stuck to their task and had their moments, particularly down the right flank.
Burns crossed accurately on to the head of Wilbraham, who could not quite grow tall enough to get over the ball, before Little’s cutback to Burns left McAuley needing to take emergency action to block the Welshman’s goalbound shot.
Burns was involved again when his cross caused panic inside the Albion box, before striking the loose ball himself with power but Foster saved at his near post.
City continued to press, but Tony Pulis’ men held firm to move into round four.