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A minute's applause was held ahead of kickoff in memory of West Ham striker Dylan Tombides, who passed away at the age of 20 yesterday following a three-year battle with testicular cancer.
Carroll stopped Palace taking the lead at the other end later in the half, clearing a Kagisho Dikgacoi header off the line.
The visitors started to dominate possession, while Yannick Bolasie, Mariappa and Dikgacoi all had further efforts to break the deadlock, but West Ham did just enough to keep them out.
West Ham believed that they should have had a penalty when Carroll fell under a challenge from Mile Jedinak, but the referee was not interested in their appeals.
Julian Speroni was tested in the Palace goal shortly before the break when Nolan and Carroll both unleashed shots in the space of a minute, but he was able to stop the home side from taking the lead.