Thirty-four minutes into the game, summer signing Mauro Zarate fired the Hammers into the lead with a superbly struck volley that left Palace keeper Julian Speroni with no chance.
Less than five minutes later, winger Stewart Downing cut in from the right wing and curled a sumptuous effort from 25 yards to double the Irons' lead.
Just two minutes after the break, James Tomkins met Downing's deep corner but the centre-back smashed his header against the bar from a couple of yards out
Immediately after Tomkins' glorious chance, Palace pulled a goal back after striker Marouane Chamakh picked up the ball from 20 yards and drilled an effort into the bottom-right corner past a sprawling Adrian.
Palace's tails were up and with an equaliser looking inevitable, West Ham went to the other end and put the game beyond doubt after Carlton Cole fired a low drive past a statuesque Speroni to make it 3-1.
Palace's second straight defeat plunged the south London club into further distress, with the board still hunting a replacement for Tony Pulis.
Hammers boss Allardyce only clung onto his job in the summer after promising the West Ham board more expansive, attacking football.
Allardyce's attacking revolution failed to bear fruit on the season's opening day in a frustrating 1-0 Upton Park defeat to Tottenham, with the Hammers spurning a host of half-chances.
Former Lazio poacher Zarate was able to cut West Ham's toothless finishing short at Selhurst Park however, capping a lively full debut with a smart first-half finish.
Former Middlesbrough wing Downing claimed just his second West Ham goal moments later, as Palace paid the price for backing off in midfield.
Downing raced down the right, cut off his flank and nudged a side-footed effort past the blameless Speroni.
James Tomkins headed against the crossbar to open the second half as West Ham sought to kill off the contest, but Palace immediately seized on the reprieve, with former Arsenal forward Chamakh firing in a low shot from 20 yards to half the deficit.
Bannan blasted straight at Adrian from the edge of the area, but just when the hosts scented level terms West Ham struck again with striker Cole, so profligate against Spurs, who pounced on a loose ball in the Palace box to lash past Speroni and kill the contest.
Palace's Co-chairman Steve Parish was joined by former Palace striker Mark Bright in the directors' box, and no doubt the pair had plenty to discuss.
Parish was all set to hand Malky Mackay the reins to replace Pulis, who walked out on the eve of the season after rows over transfer policy.
Mackay fell out of the running after the FA launched an investigation into racist, sexist and homophobic text messages sent during his time as Cardiff manager.
Tim Sherwood pulled out of the running for the Palace job after initially being deemed second choice to Mackay, leaving Millen to take charge for the second week running.
While West Ham can look towards Cole and Zarate forging a dangerous strike partnership, Palace know time is running out for transfer recruits with the window closing on September 1.
Millen has admitted he will spearhead Palace's recruitment drive in the absence of both Pulis and now Moody.
Co-chairman Parish must now act swiftly to secure a new managerial appointment however, with Palace already battling to set their season on track.
PAUL MERSON ON PALACE v WEST HAM
The Palace players look a bit lost if I’m being honest. There wasn’t a lot of shape about the team. Over the last six months if you have gone to Palace you’ve had to work very hard, but when West Ham got on top they stayed there. Palace were begging for half-time because they were all over the place.
They need to get someone in very soon or sort something out. Before the game I would have said yes to Keith Millen, but when you watch that today then maybe no. It wasn’t the Tony Pulis team. That’s the problem, he’s got to get them hard to beat again.