Palace made a bright start to this Boxing Day clash on the south coast, winning three corners and testing Artur Boruc in the opening ten minutes at the Vitality Stadium.
Damien Delaney's volley from a Jason Puncheon set piece was the Eagles' first chance of the afternoon, but the home side dealt with the effort and cleared. After that, the game slowed for a bit, with neither goalkeeper being tested too much.
Bournemouth looked certain to take the lead when Junior Stanislas' perfectly weighted cross saw Matt Ritchie and ex-Eagle Glenn Murray jump for the same ball, but it was put narrowly wide. Murray then went close to connecting with a dangerous cross in from Adam Smith, but he was a yard or so off.
The home side continued to enjoy a lot of the ball after that, with Palace not looking particularly dangerous going forward. Neither Palace nor Bournemouth really had a clear cut chance for the rest of the half and they went in level at the break.
Half time saw Yohan Cabaye's return as he replaced Jordon Mutch in midfield for the Eagles. The game began to open up in the second period and Palace began to enjoy a spell on top, probing for a way through the Cherries' backline but with little success.
The second half soon slipped back into the ways of the first, with neither side really looking more likely to take the lead than the other. It ended 0-0, with Palace settling for a point ahead of Monday's home game against Swansea City.
Palace XI: Hennessey; Ward, Dann, Delaney (c), Souare; Zaha, McArthur, Ledley (Jedinak, 73), Puncheon; Mutch (Cabaye, 45); Campbell (Chamakh, 66).
Subs: McCarthy, Kelly, Hangeland, Dymond.
AFC Bournemouth XI: Boruc; Francis (c), Cook, Gosling, Surman, Arter (O'Kane, 45), Daniels, Smith, Stanislas, Murray (Rantie, 70), Ritchie.
Subs: Federici, Pugh, MacDonald, Kermorgant, Distin.