The two London rivals both went into the game looking for a victory that would help to ease their relegation worries.
Here, Sports Mole takes a closer look at the events that unfolded at Selhurst Park.
On Target 4
West Ham United:
On Target 2
Was the result fair?
At the end of the first half, West Ham could consider themselves unfortunate to be a goal down, but the home side improved after the break and deserved their win this evening. They showed great solidarity in defence and fought for every ball. It is a display that Tony Pulis will want to build on, as he looks to keep his side in the Premier League.
Crystal Palace's performance
Palace may not have dominated the possession tonight, but they used the ball far more effectively than their opponents. In the first 45 minutes they were outplayed, but Chamakh's goal two minutes from the interval gave them added impetus and something to hang onto in the second half. The Hammers tried to play their way through the home side, but Palace's defence stood up to the task and their manager will have been proud of the passion his team displayed.
West Ham United's performance
The visitors were not at their best this evening and only managed to have two shots on target the entire game. Stewart Downing was unlucky to see a goal ruled out for a foul inside the box, but it cannot cover up their display. They were second to every ball and will have been disappointed at the amount of times they gave the ball away when in good attacking positions.
Sports Mole's man of the match
Mile Jedinak: The Crystal Palace captain was fantastic this evening and will have been delighted to help the club to win in the same week he signed a new contract. He helped stifle West Ham's midfield, whilst also posing a threat up the other end by creating numerous openings for his team. An honourable mention must also go to Bannan, whose fine delivery led to the winning goal.
With Palace a goal up and starting to come under some pressure, Cameron Jerome had the chance to give them the breathing space of a second goal. He was played through by Mile Jedinak, and with just Jussi Jaaskelainen to beat, he hit his effort straight at the keeper. It was a poor miss by a striker who needs to impress his new manager, but luckily for Palace, it didn't cost them the game.
Lee Mason had solid performance in charge this evening, in a game that was keenly but fairly contested. The goal that was disallowed will be debated by West Ham fans, however he was given no choice but to rule out the effort for a foul inside the box.
Crystal Palace: Palace welcome Cardiff City to Selhurst Park on Saturday.
West Ham United: The Hammers are also in action on Saturday and will face Liverpool at Anfield.