The home side took the lead at the end of the first half through Marouane Chamakh's headed effort
Stewart Downing had a goal disallowed for West Ham after the break, but they were unable to find an equaliser as Palace claimed a crucial victory.
Read how the action unfolded below.
7pmGood evening and thank you for joining Sports Mole for live text commentary of the Premier League match between Crystal Palace and West Ham United at Selhurst Park.
7.03pmCrystal Palace go into the game having suffered a 1-0 defeat to Norwich City at the weekend. It marked their 10th loss this season, but there was plenty of encouraging signs for fans of the club in Tony Pulis’s first game in charge.
7.06pmOne statistic that has been mentioned frequently in recent weeks, is the fact that Pulis has never been relegated in his managerial career. He has a tough task ahead of him at Selhurst Park and will be looking to invest in new players when the transfer window re-opens at the start of January.
7.07pmThe teams have been announced for this evening's game, and I can bring them to you now, starting with the hosts.
7.11pmWEST HAM SUBS: Adrian, McCartney, Jarvis, Maiga, Demel, J.Cole, Collison
7.13pmCrystal Palace remain unchanged from the team that were beaten by Norwich City at Carrow Road on Saturday. It means that Cameron Jerome and Marouane Chamakh will have a chance to impress the new boss in attack.
7.19pmWest Ham moved three points clear of the relegation zone at the weekend, after that win over Fulham. Mohamed Diame, Carlton Cole and Joe Cole were all on the scoresheet, as they ended a run of five league games without a win.
7.22pmGoing into tonight's game, Crystal Palace currently have the worst attacking record in the league. They have only managed to find the back of the net seven times in their 14 league matches. Dwight Gayle is their top goalscorer with two strikes.
7.25pmThe away side have been equally goal-shy, having scored 12 times in the Premier League this season. They have missed Andy Carroll’s threat in the box, and Ravel Morrison leads their scoring charts with three goals.
7.28pmThe Hammers' problems have certainly not stemmed from the back, as they have kept seven clean sheets already this season, which only Everton and Tottenham Hotspur can match.
7.32pmThese two teams last met in 2012 during a Championship fixture. On that occasion at Upton Park it finished goalless. Their last meeting in the Premier League was in 1998, where they played out an entertaining 3-3 draw at Selhurst Park.
7.36pmCrystal Palace have been relegated in all four of their previous Premier League campaigns. A more worrying stat for fans is that their current tally of seven points is the least they have managed after 13 games in the top flight.
7.40pmThe last time an away team won this fixture was back in April 1992, when Palace claimed a 2-0 victory at Upton Park. Since then, the home side has won on four occasions, while the other four games have been drawn.
7.42pmWest Ham fans will be wary if the home side take the lead tonight, as they are yet to earn even a point after falling behind this season.
7.46pmPREDICTION: Although Crystal Palace tasted defeat at the weekend, they were far from outplayed and showed signs that Pulis will have a real impact at the club. West Ham go into the game having claimed a fantastic home win, that will no doubt breathe confidence into the side. It will be a keenly contested encounter, with a 1-1 draw the way I see this game finishing.
7.49pmIn London derbies this season, Crystal Palace have not picked up a single point, losing all three of their capital clashes. West Ham have fared better, winning two out of their three games, most notably scoring three past Tottenham Hotspur at White Hart Lane.
7.52pmThere isn't long left until kick off here in South London, and the players are lined up in the tunnel waiting to get started.
2 minIt looks like West Ham might have a problem as O'Brien landed awkwardly, but he is back up and running for the Hammers.
4 minWe haven't seen much in the way of chances in the opening minutes of this match. There have been a lot of keenly contested challenges and attempts to pick out the forwards with long balls from the back.
6 minCrystal Palace have a spell of possession deep inside their opponents half and the ball finally comes to Ward in space, but his cross into the box is straight into the hands of the keeper.
8 minThe home side have seen plenty of the ball in the early stages of this game, without posing an attacking threat. They have the support of the ground too, with the fans in full voice this evening.
11 minDelaney is the next player to go down in painful fashion this evening, and he has to go off the pitch for treatment on his shoulder.
13 minPalace win a free kick just inside their opponents half, when Rat is penalized for climbing all over Puncheon. The ball into the middle is poor though and the home side clear.
14 minBannan has the first attempt on goal of the evening, as he takes down a long ball on the edge of the box, before getting it onto his left foot, and curling a strike over the bar.
15 minPalace are starting to ask questions of the visiting defence, and Jaaaskelainen has to be alert to keep hold of a Puncheon cross that was deflected goalwards.
17 minThe visitors have a spell of pressure of their own, and when the ball breaks to Rat on the edge of the box he fancies his chances of a long range strike. In the end though, his effort with the outside of his left foot is sliced wide.
20 minWest Ham come close to opening up Palace as Nolan tries to slip the ball into Cole, but Speroni is out quickly to make the block. The striker was offside though, and a free kick has been given to the hosts.
23 minThe Hammers have started to take control of this game and have begun to play at a higher tempo. They are unlucky to see a couple of balls into the box cleared before Cole can get a header away, and Diame has been showing some neat touches in midfield.
26 minThe visitors have won a free kick in a promising position on the left hand side, after Morrison is fouled.
26 minThe ball into the middle finds Nolan, and he spins away from his marker, before firing in a dangerous cross that the home side scramble clear.
28 minWest Ham appeal for penalty kick after the ball hits Dikgacoi's arm inside the box, but it would have been harsh on the home side as he knew nothing about it.
30 minYELLOW CARD! Morrison shows great skill to spin past Delaney, who then brings him down and picks up a booking. West Ham will have a free kick from around 25 yards out that Downing is standing over.
31 minCHANCE! Downing chips a wonderful ball into the box for Nolan, but the midfielder doesn't make good contact and scuffs it into the hands of the keeper. That was a huge chance for the visitors!
33 minMorrison is starting to see plenty of the ball, and has shown some fantastic touches inside the Palace half. He is a player that Pulis's men will have to keep a firm eye on.
35 minCHANCE! What a chance for West Ham! Cole is played through down the left hand side, before playing the ball back across the box to Downing, but it was delivered behind the midfielder and Palace are able to clear.
38 minCHANCE! Downing picks up the ball on the right hand side, and his cross into the middle is headed over by Diame. The Hammers are in full control here and all they need now is a goal.
41 minPalace have a good chance to get something at the end of the half, as Ward sees his powerful shot deflect wide for a corner.
42 minGOAL! Crystal Palace 1-0 West Ham United (Chamakh)
42 minPalace have taken the lead at the end of the half! Bannan's initial corner kick was poor and failed to beat the first man, but it comes back out to him, and this time his cross headed into the back of the net by Chamakh.
44 minAfter being on the back foot for much of the half, that goal has given the home side a huge lift, and the fans are understandably ecstatic!
45 minThere are going to be two minutes added on at the end of the half.
45+1 minWest Ham break forward and the ball falls kindly to Downing inside the box, but his volley is brilliantly blocked by Delaney. The ball goes out for a corner, but Speroni manages to punch it clear.
45+2 minHALF-TIME: Crystal Palace 1-0 West Ham United
8.50pmWest Ham were arguably the better team in the first half, but it is Palace who have the lead thanks to Chamakh's late goal. A lot of the credit has to go to Bannan for his whipped ball into the middle that created the chance.
8.53pmThe first half stats show that West Ham had more of the ball, with 55% of the possession. They managed six strikes on goal to Palace's five attempts, but as things stand the home side lead.
8.56pmIf Palace manage to hold onto their lead, they will move up one place to 19th, but draw level on 10 points with Fulham. Their goal difference is just two behind the Cottagers, so they may well overtake them by the end of the next 45 minutes.
9pmSam Allardyce may be thinking of making some changes for the second half. His substitutes made a huge difference at the weekend and Joe Cole and Modibo Maiga are two of the players on the bench who could be introduced to the action.
9.02pmThe players are making their way out onto the pitch and we will be back underway soon.
48 minThere hasn't been any attempts on goal so far in the half, but West Ham are keeping hold of the ball well and are looking to pass their way up the pitch.
50 minDiame has the first shot on goal of the second half, but his strike from out wide misses the target.
51 minCHANCE! Jerome latches onto the end of a long ball and does well to pull it back to Puncheon on the edge of the box, but his effort is palmed wide by Jaaskelainen.
52 minCHANCE! From the resulting corner, Bannan's ball into the box is headed over by Dikgacoi.
52 minCHANCE! Palace have missed a golden chance to make it 2-0! Jerome is slipped through on goal down the left hand side, but his low effort is hit too close to Jaaskelainen, and the keeper makes the save.
55 minThe hosts have started this half fantastically, but they will rue their missed chances if the Hammers manage to find an equaliser.
58 minSUBSTITUTION: It's a double change for West Ham, as Joe Cole and Maiga are on for Carlton Cole and Nolan.
60 minWest Ham look a bit out of sorts at the moment, and are giving the ball away too easily.
62 minGOAL DISALLOWED! Downing has the ball in the back of the net after lashing home a strike following a long free kick into the box, but it has been disallowed for a foul.
67 minYELLOW CARD! Tomkins picks up a booking for a late tackle on Jerome, and Palace have a free kick in a promising position.
68 minCHANCE! Bannan whips another wonderful ball into the middle, that Jedinak pulls back across the box, before it is tapped into the net. The goal is ruled out though as Jedinak was offside when the free kick was taken.
71 minThe groundsman has just had to mend the nets, which had come loose from the post. They are fixed now and we are back in play!
74 minDiame bursts through the midfield and shows a clever piece of skill to get away from Jedinak who then brings him down. They have a free kick in a good shooting position and will be desperate to test the keeper here.
75 minCHANCE! Downing takes the kick, and aims for the bottom right hand corner, but the ball lacks enough power to beat the keeper, who claims it with ease.
77 minCHANCE! Palace steal the ball in midfield and look to break quickly. It is eventually played into the path of Dikgacoi, who tries his luck from long-range, but his effort is hit straight at Jaaskelainen.
79 minCole is within inches of latching onto a threaded pass by Diame, however the ball is just out of his reach and the keeper is able to gather.
82 minSUBSTITUTION: Palace make a change with O'Keefe replacing Bannan, who receives a standing ovation.
83 minWest Ham have kept trying to play their way through the Palace defence, with the home side remaining resilient so far. They have just a few more minutes left to hold on and claim a precious three points.
85 minSUBSTITUTION: The goalscorer Chamakh makes way and Williams comes on in his place.
87 minJerome looks to be struggling, but he will have to stay on the pitch as Palace have made all three of their changes.
88 minCollins bursts forward from the back and wins his side a free kick just inside the Palace half. This is a big chance to get the ball into the box and test the defence.
88 minNobles ball into the middle is headed out and West Ham will have a throw in deep inside their opponents' half.
89 minPalace hold firm yet again and they are able to clear the ball away before it gets delivered into the box.
89 minCHANCE! West Ham win a corner and Collins manages to get his head to ball, but his effort deflects of Jedinak and goes out of play. The referee didn't spot that it came last off the Palace man though and gives a goal kick.
90 minWe are going to have five minutes of injury time.
90+3 minMorrison slips a wonderful pass through to McCartney, but he is offside when he attempts to play the ball back across goal. It was a tight call, but the assistant got that correct.
90+3 minCHANCE! Jaaskelainen comes out to collect a long ball, but gets nowhere near it. It drops to Kebe who should put the ball into the net, but fires his effort over the bar!
90+5 minFULL-TIME: Crystal Palace 1-0 West Ham United
9.54pmWhat a win for Crystal Palace! They move off the bottom of the table thanks to a header from Marouane Chamakh. West Ham will be disappointed not to have built on the weekend's win over Fulham, and created very little in the second half.
9.56pmCrystal Palace move up to 19th in the table and are level on 10 points with Fulham. The fans will be delighted that Tony Pulis's first home game as manager has got off to a winning start.
9.58pmThat's all we've got time for here tonight. Please stay with Sports Mole for all of the latest news, but from me, it's goodnight!