Palace have won all five of their matches on the road since Pardew took the helm, with Saturday's triumph - completed with 10 men on the field as Glenn Murray was dismissed - giving his charges a comfortable advantage over the bottom three.
When Pardew took Newcastle United to West Ham back in October, Aaron Cresswell's goal proved decisive - but the defender had a very different impact this time around.
In attempting to clear a tame Murray header from Jason Puncheon's corner, Cresswell succeeded only in sending the ball spinning into his own net on the stroke of half-time.
Allardyce's mood will have darkened significantly just six minutes into the second half when his side failed to defend another Puncheon corner, with Scott Dann profiting to head home from close range.
Enner Valencia reduced the deficit with a superb late strike, but Palace exacted revenge for August's 3-1 home loss against West Ham.
It was the hosts who threatened first, Mark Noble's 14th-minute free-kick casting Julian Speroni in the role of mere bystander, but striking the crossbar.
Palace's first clear sight of goal came midway through the half as Murray - one of four changes for the visitors - collected Puncheon's pass before slicing his shot wide of the target.
Cresswell stuck out a boot to deal with Murray's header, but the ball skewed into the net as the Palace forward took full advantage of his initial let-off from referee Mike Dean.
Things went from bad to worse for Allardyce early in the second half as Puncheon's corner was headed in by the unchallenged Dann, while Murray's header was followed six minutes later by his dismissal.
Valencia's 20-yard strike allowed West Ham a strong finish but, after Carl Jenkinson and the Ecuadorian were denied late on, the hosts saw their winless run extended to six games.
