Substitute Saido Berahino's first-half strike, his second in the Premier League, handed the hosts the advantage and Gareth McAuley sealed the result seven minutes from time.
Palace, who saw manager Ian Holloway resign on October 23, remain rooted to the foot of the table under the guidance of caretaker boss Keith Millen.
But West Brom, who picked up just their third win of the league campaign, are heading back in the right direction after ending a three-game winless run.
The victory came despite manager Steve Clarke being forced into three changes from the 4-1 loss to Liverpool, with James Morrison replacing Claudio Yacob, while Nicolas Anelka and Victor Anichebe were forced out with illness and injury respectively.
Millen was able to field the same side that lost 2-0 to Arsenal in his first game in charge last weekend.
The visitors had the best opportunity of the opening 10 minutes, with Marouane Chamakh finding Adlene Guedioura, who fired his effort straight at Boaz Myhill.
It proved to be the Algeria international's last meaningful input as he was carried off on a stretcher following a collision with Myhill less than 10 minutes later.
He was replaced by Jason Puncheon but it was another substitute who made the difference on the stroke of half-time, Berahino putting the hosts ahead.
On for the injured Billy Jones only 13 minutes earlier, the 20-year-old converted from Stephane Sessegnon's pass a minute before the break, finding the bottom corner to take his tally for the season to six in all competitions.
The home side came out with the same vigour in the second half and saw a chance to double their advantage go amiss in the 51st minute as Morgan Amalfitano's dangerous ball narrowly eluded Sessegnon and Shane Long.
They continued to dominate as the minutes ticked by, but Palace almost managed to get one of their own against the run of play just 10 minutes later as Puncheon forced Myhill to tip over the bar with a powerful strike.
Their increasingly desperate efforts ended up being in vein come the 83rd minute, though, as McAuley jumped highest to head a corner past Julian Speroni and put the result beyond doubt.
