The home side had the better of the first half at Vicarage Road, Stefano Okaka coming closest when his header hit the crossbar four minutes in.
Eagles goalkeeper Wayne Hennessey produced a good save as Joel Ward inadvertently diverted Troy Deeney's cross towards his own goal.
Palace grew into the match in the second half and Luka Milivojevic's free-kick struck the crossbar just after the hour mark.
James Tomkins then hit the post before the ball was hooked clear by Troy Deeney.
Palace move up to 15th, six points ahead of 18th-placed Southampton. Watford are in 12th, three points better off.
Watford: 30 April v Spurs (A)
Palace: 28 April v Leicester (H)