Blues were made to pay for some sloppy defending as they fell to a narrow defeatBCFC
Pep Clotet's side twice took the lead but were pegged back on each occasion before Albion substitute Charlie Austin claimed all three points for the visitors with his second goal of the afternoon.
Lukas Jutkiewicz and Harlee Dean were on target for the hosts, with Grady Diangana scoring one for the visitors and substitute Austin bagging a brace.
Blues made the perfect start, with Jutkiewicz heading home a corner after just three minutes, before Diangana levelled seven minutes later.
But despite taking the lead for a second time during the second-half through Dean, Austin levelled just minutes after entering the fray with an excellent finish, before heading the winner late on.
There were three changes to Blues starting line-up with Geraldo Bajrami, Lukas Jutkiewicz and David Davis replacing Wes Harding, Jacques Maghoma and Josh McEachran.
It was first league start for 20-year-old Bajrami, an Albania Under-21 international.
On a brisk early afternoon at the St. Andrew's Trillion Trophy Stadium, Blues began the game kicking towards the away support massed in the Gil Merrick Stand.
Blues made a lively start and fashioned their first attempt less than three minutes in when Jude Bellingham saw his shot from the edge of the area deflected behind for a corner.
The resultant deadball was cleared but only as far as Maxime Colin who sent in a sweet cross from the right which was met by Jutkiewicz who powered home his header.
The hosts came close to doubling their advantage two minutes later as Colin got through on the by-line before pulling the ball back to Alvaro Gimenez at the near post.
But the Spaniard directed his shot just the wrong side of the upright
However, Blues' advantage didn't last long as West Brom equalised on the 10-minute mark and once again the goal stemmed from a corner.
Matheus Pereira's corner reached Matt Phillips who then fired the ball across the Blues box, where Grady Diangana sidefooted it home at the back post.
In a game which was ebbing and flowing, Bellingham burst forward with the ball before curling a 25-yard effort over the bar.
Colin then tried his luck from a similar distance, with the same outcome.
Blues were awarded a free-kick in a dangerous position on the right hand side of the box after Jefferson Montero was brought down. The same player stepped up and let fly with a powerful shot, which was punched away by Sam Johnstone in The Baggies goal.
As the half entered its final 15 minutes it was Albion that started to pose a real attacking threat, with Blues struggling cope with their pace on the break.
But when they did get the ball into the Blues box the home defence did well with some last-ditch tackles and clearances.
With 40 minutes played Albion were forced into a change when goalscorer Diangana limped off, with Kyle Edwards sent on in his place.
With the game into stoppage time at the end of the half, Blues very nearly regained their lead.
A sublime looped ball over the top by Bellingham found Pedersen, but with just the goalkeeper to beat he didn't quite get his shot off well enough and stabbed it straight at Johnstone.
Half-time: Blues 1 West Brom 1
Blues came out of the blocks swiftly and won themselves a corner thanks to some good work by Jutkiewicz.
Bellingham swung the ball in from the left, but it was deflected behind.
But Blues made no mistake at the second time of asking.Another precise deadball was this time met by defender Dean who got in behind before looping a header home past Johnstone.
With the game progressing it was becoming quite a tasty affair with challenges flying in from both sides.
Blues won a free-kick in a dangerous position 25-yards out from the centre of the goal. Bela stepped up but curled the chance a couple of yards over the bar.
Albion made their third and final substitution of the afternoon when Charlie Austin came on for Phillips after 69 minutes.
And just minutes later Austin announced himself with a brilliant equaliser against the run of play.
He received the ball on the edge of the Blues area before swivelling and drilling a fine finish into the top corner of the net.
Things then then went from bad to worse for Blues as Austin headed Albion into an unlikely lead on 81 minutes when Austin met Furlong's cross and nodded the ball into the bottom
Blues began to throw everyone forward in search of an equaliser.
David Davis forced Johnstone into a save, before Bela headed over a decent chance.
Blues were continuing to press and from a corner Pedersen diverted the ball into the side netting but they unable to find that final breakthrough.
Blues (4-2-3-1): Trueman, Pedersen, Colin, Jutkiewicz, Bela (Montero, 84), Dean, Bellingham (G Gardner, 74) Gimenez, Davis, Sunjic (McEachran, 84), Bajrami.
Subs (not used): Camp, Harding, Villalba, Maghoma.
Bookings: Jutkiewicz (52), Sunjic (59)
Goals: Jutkiewicz (3), Dean (47).
West Brom (4-2-3-1): Johnstone, Robson-Kanu, Bartley, Ajayi, Livermore, Phillips (Austin, 69), Pereira, Townsend (Furlong, 61), Sawyers, Diangana (Edward, 40),
Subs (not used): Bond, Krovinovic, Barry, Hagazi.
Bookings: Livermore (57).
Goals: Diangana (10), Austin (73, 80)
Referee: Darren England.
Attendance: 20,796 (2,768 West Brom fans)