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The home side could have been in the lead after just two minutes played, as Ahmed Elmohamady sent an inch-perfect cross towards Nikica Jelavic at the back post, but the Croatian's header flew wide of the target.
The Eagles then won a free kick on the edge of the box a few minutes later, but Mile Jedinak curled his effort over the bar.
The game went through the motions throughout the majority of the first half, with the action mostly congested in midfield.
The hosts, however, had another great chance to break the deadlock with five minutes left of the opening half after putting together a good spell of pressure inside the Palace final third.
After several crosses were cleared away by the Eagles, the ball dropped to Mohamed Diame, who exchanged passes with Abel Hernandez before firing in a low strike across goal that flew just wide of the far post.