Aliadiere scored his fourth goal of the competition to seal Arsenal's success after Nigerian international Nwankwo Kanu had given the Gunners a first-half lead.
But Arsene Wenger's side were flattered by the final scoreline as Albion dominated the game for spells, hit the woodwork twice, and tested a strong Arsenal team to the limit.
Wing-back Neil Clement tested Arsenal goalkeeper Graham Stack with a stinging 25-yard free-kick after 13 minutes before Rob Hulse stabbed the ball wide from close range two minutes later.
Clement hit the bar with a cross shot in the 19th minute as Arsenal successfully rode their luck before rocking Albion with Kanu's 25th minute strike - his second goal of the season, both of which have been in the Carling Cup.
Lauren lifted a right-wing cross into the area that picked out the unmarked Kanu. His first attempt, a header from six yards, was beaten away by goalkeeper Russell Hoult.
But with Hoult grounded after his first save, Kanu had the simple task of stabbing the rebound home from close range.
Albion could have buckled after the disappointment of slipping behind, but they launched a determined bid to grab an equaliser.
They were unlucky not to win a 30th minute penalty when Andy Johnson was pulled down by Martin Keown.
Clement was again inches wide with a long-range free-kick after 34 minutes before Hulse saw his overhead kick saved by Stack just before half-time.
Albion continued to press at the start of the start of the second period with Stack again denying Hulse before substitute Lee Hughes fired over the bar when well placed.
But Albion's comeback hopes were extinguished when a mix-up between Hoult and Thomas Gaardsoe gifted Aliadiere his 57th minute clincher.
Hoult was caught out by a back pass from Gaardsoe and as he attempted to push the ball upfield he was dispossessed by Aliadiere who had the simple task of pushing his shot into an empty net.
Albion's frustration was them summed up five minutes from time when Scott Dobie beat Stack with a 20-yard drive only to see his shot cannon off the bar.