TWO late goals from in-form Graham Dorrans and sub Chris Wood ended Huddersfield's proud unbeaten home record and booked Albion's place in tomorrow's FA Cup fourth-round draw.
Dorrans' third goal in less than a week broke the deadlock in the 79th minute and completed his set of scoring in each of the three domestic competitions this term.
And Wood sealed victory at fortress Galpharm Stadium with his second-ever Baggies goal just three minutes later.
Albion controlled a largely uninspiring first half but failed to convert their dominance into a goal.
The tie livened up after the break, with Marek Cech hitting the post for the visitors and the Terriers forcing the recalled Scott Carson into action on several occasions.
But Albion's superior finishing saw them overcome the League One high-fliers.
Roberto Di Matteo made five changes as Carson returned between the sticks from suspension and Shelton Martis, Filipe Teixeira, Youssouf Mulumbu and Roman Bednar earned recalls.
Dean Kiely, Luke Moore and Jerome Thomas dropped to the bench while Gianni Zuiverloon was sidelined through illness and Abdoulaye Meite missed his first match since reporting for African Nations Cup duty with Ivory Coast.
After an uneventful opening to the game, Dorrans should have opened the scoring in the 14th minute when he stole in on Chris Brunt's right-wing centre - only to volley over from close range with the goal gaping.
The Baggies broke out of defence with a quick counter-attack in the 28th minute and Dorrans picked out Brunt on the right with a pinpoint diagonal ball.
The Northern Ireland international stepped inside but curled an 18-yard effort past the far angle of post and bar.
The visitors were dominating possession and Carson was not called into action until the 34th minute when Lee Novak nodded Michael Collins' mishit shot goalwards, but the Baggies keeper easily gathered above his head.
Six minutes before the break, Simon Cox spread the ball out to Brunt on the right and he again dipped his shoulder before unleashing a fierce 20-yard drive which Alex Smithies did well to turn around his left-hand post.
Good Albion play down the left in the 42nd minute resulted in Cox exchanging a one-two with Bednar on the edge of the box but Smithies was alert to the danger and smothered the ball at the former Swindon striker's feet.
Referee Kevin Wright waved away Terriers penalty appeals in the final minute of the half when Jordan Rhodes went down under Martis' challenge from Novak's dangerous right-wing cross.
Huddersfield looked a rejuvenated side after the interval and, two minutes into the second half, Collins headed wide from a Gary Roberts free-kick when he should at least have hit the target.
Back came Albion and Bednar's header dropped perfectly for Cech on the edge of the box and the Slovakia international swivelled before crashing a volley off the left-hand post, with Smithies beaten.
A minute later, Collins hooked on a right-wing cross to the unmarked Roberts 12 yards out and the Baggies needed Carson to be at his best to block the Town midfielder's effort at point-blank range.
The hosts had another golden opportunity in the 64th minute when Antony Kay nodded the ball down for Rhodes who shot just wide of the left-hand post from 18 yards.
Two minutes later, Di Matteo made a change as Robert Koren returned from a month-long lay-off after a hernia operation to replace Teixeira.
Collins wriggled inside Cech in the 69th minute and shaped a goalbound shot with the outside of his boot that Carson held low down.
At the other end, Martis looped Brunt's right-wing corner goalwards and Smithies just managed to punch clear under pressure from Jonas Olsson.
The game was becoming something of an end-to-end encounter and Anthony Pilkington flashed a dangerous ball across the Baggies' six-yard box which dropped for Roberts and his snapshot was gathered at the second attempt by Carson.
Huddersfield had had their chances - and Albion punished them for not taking them 11 minutes from time.
A terrific move starting on the edge of the Albion box and involving Koren and Bednar resulted in Brunt slotting Dorrans clean through.
The Scotland international out-paced Peltier before coolly tucking the ball past Smithies and into the bottom right-hand corner of the net - to send the impressive travelling Albion support behind the goal into raptures.
It was game over three minutes later when Brunt again turned provider by sliding in sub Wood and the New Zealand striker held off Nathan Clarke before forcing the ball past Smithies.
HUDDERSFIELD (4-4-2): Smithies; Peltier (Drinkwater 79), N Clarke, P Clarke, Skarz; Pilkington, Collins, Kay, Roberts (Robinson 85); Rhodes, Novak (T Clarke 58). Subs not used: Glennon (gk), Butler, Ainsworth, Simpson.
ALBION (4-4-2): Carson; Jara, Martis, Olsson, Cech; Brunt (Reid 88), Mulumbu, Dorrans, Teixeira; Bednar (Koren 66), Cox (Wood 75). Subs not used: Kiely (gk), Moore, Thomas, Samuels.
GOALS: ALBION - Dorrans (79), Wood (82).
BOOKINGS: ALBION - Brunt (foul 45).
REFEREE: K Wright (Cambridgeshire).
ATTENDANCE: 13,472 (2,392 Albion fans)
ALBION STARMAN: Graham Dorrans.