The striker netted either side of half-time, before then being given his marching orders after picking up his second yellow card 21 minutes from time.
By that stage of the match Palace were already 3-0 ahead, with centre-back Scott Dann powering home yet another header from a set piece in between Murray???s brace.
And despite West Ham forward Enner Valencia pulling a goal back after 76 minutes, it was too little, too late as far as the home team were concerned.
However, anything other than a Palace victory would have been harsh on Alan Pardew???s side, who recorded a club-record third Premier League away win in a row in the process.
The visitors dominated the contest against a lacklustre West Ham until Murray???s late red card, with the frontman guilty of spurning numerous presentable openings before eventually giving his team a deserved lead four minutes before the break.
West Ham boss Sam Allardyce will be furious though with the manner of Palace???s opener, especially after highlighting Palace???s threat from set plays before the game, only for his players to fail to deal with Jason Puncheon???s left-wing corner, before Murray???s header somehow got past both Adrian and Aaron Cresswell on the line.
But if that goal was bad enough, then Palace???s second six minutes after the break was even worse as Dann beat opposite number Winston Reid to another Puncheon corner, before bulleting a header past a helpless Adrian.
And the game was then over as a contest when 12 minutes later Murray, who was only starting up front due to injuries to first-choice forwards Fraizer Campbell, Marouane Chamakh and Yaya Sanogo, got a glancing header to Puncheon???s free kick from the left-hand corner of the box.
West Ham, who were unlucky not to have taken the lead when Mark Noble???s 20-yard free kick hit the bar after just 15 minutes, then threw the kitchen sink at their London rivals in the final 15 minutes as they sought to exploit their one-man numerical advantage.
And they came close on several occasions to making it a truly nervous finale after Valencia???s long-range strike had given them initial hope.
However, substitute Nene hit the outside of the post with virtually his first touch in English football, before Carl Jenkinson was denied by Julian Speroni at his near post and Valencia then fired just over with a curler from distance at the death.