Aliadiere struck once in each half for an Arsenal side that showed ten changes to the team that had beaten Reading last weekend.
But, even without their star names, Arsene Wenger's side were still a touch too classy for Albion whose run of four straight wins came to a resounding halt as they crashed to their first defeat under the control of new boss Tony Mowbray.
The pace of Theo Walcott and Aliadiere was a constant problem for Albion, who themselves had made six changes to the side that had started last Sunday's 3-0 win against Wolves.
Albion had scored 19 goals in their previous six games but they struggled to carry any consistent threat against an Arsenal side who have run into a rich vein of form.
The success against Albion was their eighth in nine games – the only match they have failed to win in that spell was against CSKA Moscow in the Champions League.
With both teams fielding much changed line-ups, it was Albion who were the quicker to settle.
Richard Chaplow forced Manuel Almunia into an early save while Jonathan Greening saw his snap-shot fly wide.
But the pace and trickery of Arsenal, chiefly through Walcott and Aliadiere, was always a threat.
Walcott's 17th minute cross was deflected wide by Steve Watson and from the resulting corner Alexandre Song flashed a volley inches over.
While Albion again threatened when Almunia punched away a free-kick from Nathan Ellington, it was no great surprise when a surging Aliadiere run resulted in Arsenal breaking the deadlock in the 34th minute.
The Frenchman was pursued into area by three Albion defenders and, when Watson sent him tumbling, referee Martin Atkinson had no hesitation in pointing to the spot.
Aliadiere picked himself up and placed his penalty beyond the outstretched left hand of recalled goalkeeper Russell Hoult.
That effectively signalled the end of Albion's challenge and Arsenal booked their place in the fourth round just four minutes into the second half.
Left-back Paul Robinson was penalised for hauling down Walcott on the left-hand edge of the Albion area.
Walcott whipped in the resulting free-kick and Aliadiere reacted quicker than the Albion defence to calmly side-foot the ball home beyond the helpless Hoult from 12 yards.
Greening briefly raised Albion hopes when his 54th minute volley flashed across the goal.
But Arsenal were in cruise control now and Aliadiere was denied a hat-trick after 68 minutes when Hoult halted his powerful run with a smart save.