Superior finishing proved to be the difference as Town's first experience of competing against Premier League opposition ended in defeat.Strikes inside the first 22 minutes from Rekeem Harper and Hal Robson-Kanu demonstrated the quality West Bromwich Albion had in their disposal, both attempts finding the corner from considerable distance.
At 2-0, Town pushed for a way back into the game, but some clever wing play from Kyle Edwards to set up Callum Robinson ended any hopes of a comeback.
Simon Weaver sprung no suprises with his line-up, naming the same XI that started at Roots Hall on Saturday, though there was an addition to the bench in the form of Brendan Kiernan.
The Baggies line-up featured well known names such as Charlie Austin, Robson-Kanu and Kamil Grosicki, while Slaven Bilic handed first appearances to David Button, Lee Peltier and Cédric Kipré.
Town showed no signs of stagefright at the 27,000 capacity Hawthorns, making a positive start to the game and pressing their higher ranking opponents high up the pitch.
The encouraging start was undone in the 18th minute though as Rakeem Harper fired into the corner from 25 yards out, in what was the evening's first attempt on goal.
Grosicki had the chance to double his side's lead moments later, but the Poland international was met by Joe Cracknell who made himself big and blocked the attempt.
There was nothing Cracknell could in the action that followed as Robson-Kanu dropped into space before curling past the Town stopper from 25 yards, increasing his side's advantage with a second quality finish of the evening.
Despite the two-goal deficit, Town continued to apply pressure to their hosts as Aaron Martin headed towards goal from a dangerous George Thomson delivery.
Town ended the half on the attack, but went into the break two goals behind thanks to some excellent finishing, worthy of the Sky Sports cameras capturing the action.
It could have been three for the hosts at the start of the second 45 as Kyle Edwards burst free down the left hand side and centred, though both Austin and Robson-Kanu had made the same run to the near post and Town cleared the danger.
Austin should have had his name on the scoresheet in the 65th minute after Matt Phillips had set him up with an almost open goal to aim at, though Warren Burrell was able to make a vital goalline clearance.
The Baggies' third arrived thanks to a great bit of wing play from Edwards, whose quick feet got the better of Burrell and teed up Callum Robinson who couldn't miss from a yard out.
Town: Cracknell, Fallowfield (Jones 63), Falkingham, Smith, Burrell, Thomson, Beck (Stead 61), Martin, Kerry (Kirby 79), Muldoon, Hall
Subs not used: Kiernan, Walker, Minter, Lokko
West Bromwich Albion: Button, Peltier, Kipre, O'Shea, Townsend, Edwards, Field, Harper, Grosicki (Phillips 55), Austin (Robinson 63), Robson-Kanu (Swayers 61)
Subs not used: Bond, Furlong, Ajayi, Soule
Goals: Harper 18, Robson-Kanu 22, Robinson 77
Referee: T Bramall