Superb goals from Serbia midfielder Luka Milivojevic and Wilfried Zaha twice put Palace in the driving seat but the home side hit back through second half substitutes Lys Mousset and King after they both came on in the 62nd minute.
After a dour first half, Milivojevic celebrated his 27th birthday with a brilliant free kick from 25 metres in the 47th minute which left Bournemouth keeper Asmir Begovic clutching nothing but thin air.
Begovic then kept out a sitter from Patrick van Aanholt when the Palace defender was put through by a brilliant pass from Zaha and his poor finish would ultimately prove costly.
The visitors were swiftly punished as Mousset levelled in the 65th minute after curling a fine low shot past Wayne Hennessey after the Palace keeper had also made two good saves in quick succession.
Livewire Zaha then produced a moment of magic ten minutes later as he turned his marker with dazzling footwork before unleashing a stinging shot from 18 metres which sailed past Begovic after taking a slight deflection off Lewis Cook.
But Palace, who have made it a habit to concede late goals this season, once again failed to hold on and King salvaged a point for Bournemouth from close range after a corner was headed into his path.
(Writing by Zoran Milosavljevic; Editing by Christian Radnedge)
