Striker Josh King put Bournemouth ahead with a neat finish after 11 minutes and Palace wasted a great chance to equalise when Yohan Cabaye's penalty was well saved by a diving Artur Boruc.
Bournemouth had chances to extend their lead but Dann rose high to power home Jason Puncheon's cross and secure Palace's first point of the season.
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(Reporting by Ed Osmond,; Editing by Neville Dalton)
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