Early goals from Fitz Hall and Andy Johnson ruined Gary Megson's game plan of using three centre-backs and Johnson's third for Palace early in the second half gave Iain Dowie's Eagles a thoroughly deserved win.
The Baggies were well and truly blasted as Palace made a blistering start with two goals in the first 12 minutes.
Albion should have cleared Wayne Routledge's corner better, but instead Ben Watson was allowed to return the ball to Routledge on the right flank and this time his cross eluded the crowded goalmouth to find Hall at the far past.
The former Oldham star forced a low header past Russell Hoult's outstretched left hand as the ball nestled neatly in the bottom corner of the net.
The Baggies had a great chance to reply instantly when Robert Earnshaw's corner from the right caught Hungarian keeper Gabor Kiraly out of position but Darren Moore's header bounced once and over the crossbar.
Albion had another setback seven minutes later after a breathtaking passing movement had the visitors reeling.
After playing their way out of defence, Michael Hughes took over the proceedings and played a superb pass to Joonas Kolkka.
The flying Finn accelerated past his marker and drove a low cross into the goalmouth only for Martin Albrechtsen to drag down Johnson as the Palace striker had the goal at his mercy. Johnson picked himself up and placed the spot-kick perfectly into the left corner of the net to put Palace into a two-goal lead.
Palace were winning every 50-50 ball and chances were being created for Danny Granville and Johnson.
Albion struggled to make any impact and were relieved to hear the half-time whistle.
The second half started with Albion attempting to get themselves back into the game. They had a great chance in the first few minutes after the restart when Riccardo Scimeca's cross from the right found Earnshaw who hesitated and blasted his shot against the crossbar from only eight yards out.
Johnson sealed all three points with a third goal in the 50th minute. A clever flick from Kolkka on the halfway line saw him go past Bernt Haas. He in turn found Johnson and the Palace hitman stormed towards the edge of the area before letting fly with a low shot which struck the foot of the post before rolling over the line.
The third goal took the game out of Albion's reach and the match lost much of its intensity as a result.
Kanu was ineffective and sometimes downright lazy while Earnshaw was wasteful. Only Hungarian midfielder and captain Zoltan Gera and Darren Moore could hold their heads up and come away from the game with any merit.
Indeed Gera had a good chance to score but in his frustration fired over the bar while Moore headed wide from Gera's corner.
Albion nearly gave away a fourth goal when Haas' poor pass was intercepted by Johnson.
However, Moore's recovery was miraculous as he got back to tackle.
As Palace slowed the game down, Albion got more and more frustrated and Earnshaw again missed a good chance.
However, Johnson was always a real handful for the Baggies defence and was a fraction away from his hat-trick when he just failed to get on the end of Vassilios Lakis' cross from the left.
Right at the end Dougie Freedman was put clean through but he waited too long and Moore again got back to make another crucial tackle.
But by then the Palace fans were rubbing their hands as they looked forward to their next home match against Arsenal.
MAN OF THE MATCH: Michael Hughes (Crystal Palace) - Had a hand in the move that led to Palace's penalty and was a calming influence throughout.