Eunan O’Kane and Callum Wilson helped the Sky Bet Championship side make club history for the second time in four days.
O’Kane fired in the opener, only for a deflected Georgios Samaras shot to gift Albion a late equaliser, leaving substitute Wilson to race clear and blast Bournemouth’s winner.
The Cherries thumped Birmingham with a record 8-0 victory to climb to fourth in the table on Saturday – then stunned their top-flight opponents to tread new ground in the League Cup.
Both managers lodged their ‘concentrating on the league’ excuses early, making 10 changes apiece from weekend line-ups.
The visitors proved the less interested and inspired in a hectic first half lacking only in gilt-edged chances and goals.
Liam O’Neil shaved a free header wide when full contact would have opened the scoring against the run of play for Albion.
Boaz Myhill was forced to parry from Tokelo Rantie after a Junior Stanislas raid, but still the final touch eluded Eddie Howe’s men.
Youssouf Mulumbu was booked for a professional foul on Rantie as the half drew to a close, but again the hosts were unable to bring fine pressure to bear.
Sebastian Blanco fired over the bar as Albion opened the second half brightly, but it was the hosts who broke the deadlock. Stanislas drove through the middle, capitalising on West Brom backing off to thread the ideal ball to O’Kane.
The onrushing midfielder calmly picked his spot and side-footed past a despairing Myhill.
Republic of Ireland Under-21 cap O’Kane’s goal was the least Bournemouth deserved for their industry and ingenuity in the face of supposedly-superior opposition.
Albion rallied, through shock if anything, Blanco denied a tap-in by Elphick’s sliding block, both the Cherries skipper and referee Paul Tierney waving away lacklustre handball shouts.
Albion were shortly playing down a penalty claim themselves, when Gareth McAuley took Rantie’s drive into the midriff.
The hosts escaped with a slice of fortune when referee Tierney denied the Baggies a penalty despite keeper Lee Camp seemingly upending Victor Anichebe.
Stephane Sessegnon replaced the ineffectual Ideye for West Brom, with Samaras and Saido Berahino also answering the cavalry call.
Samaras’ deflected shot scrambled Albion level against the run of play, with Elphick taking the unwanted credit.
But just when the visitors were wiping the collective brow, Bournemouth broke at pace, and replacement Wilson blasted home to wrestle back the lead and score the winner.