An early Deqwon Ebanks strike and well-taken second-half goals from Charlee Adams and Reece Brown ensured a place in the fourth-round draw to be held on 14 December.
Despite seeing West Bromwich Albion battle back to draw level before half-time, Blues outplayed their opponents in all areas of the park and thoroughly deserved to progress further in the competition.
Steve Spooner's youngsters showed plenty of energy throughout to limit the Baggies to few chances, particularly in the second-half.
Blues striker Ebanks got his side off to a flyer when he pounced on a rebounded shot to blast home from six yards after just four minutes.
Despite the early opener, Blues didn't take their foot off the pedal. Winger Demarai Gray saw a stinging shot from distance tipped over by Albion 'keeper Alex Palmer before Ebanks blasted over just inside the area after being teed up by Reece Hales.
The Baggies' first effort on goal came in the 24th minute but it was comfortable for Blues goalie Nick Townsend to scoop up Rees Wedderburn's free-kick.
West Brom did threaten to ruin their opponents' positive start when Aaron Birch stabbed home a 36th minute equaliser after Wedderburn's cross-cum-shot had been tipped into his path by Townsend.
However Spooner's charges weren't prepared to let this tie slip away and, after right-back Joshua Dacres-Cogley had threatened with a tricky run inside in the 48th minute, Blues stunned West Brom with two goals in as many minutes.
A well-worked attacking move was clinically finished by Adams inside the Albion area in the 56th minute before Brown fired home in style from 25 yards moments later.
Blues easily saw out the rest of the encounter and although Albion substitute Ged Oldnall had an injury-time effort ruled out for offside, the outcome of the tie never looked in doubt.
Blues U18s: Nick Townsend, Joshua Dacres-Cogley (Viv Solomon-Otabor 90+2), Bobby Moseley, Reece Brown, Jean Kalenda (Callum Thomson 85), James Fry (C), Charlee Adams, Liam Truslove, Reece Hales, Deqwon Ebanks (George McGee 82), Demarai Gray.
Subs not used: Callum Preston, Raekwon McFarlane.
West Bromwich Albion U18s: Alex Palmer, Jordan Francis (Daniel Barrow 78), Tom Smart, Wesley Atkinson, Kieran McCalla (Reiss Greenidge 60), Callum Jones, Ryan Pace (Ged Oldnall 60), Aaron Birch, Alex Jones, Samir Nabi, Rees Wedderburn.
Subs not used: Matthew Buchanan, Joel Ambalu.