Everton dominated the game in terms of possession but they were unable to force a lead in a match of few chances at either end.
The game didn’t start well for the away side as key midfielder Steven Pienaar went down injured inside the second minute, setting up a scrappy first ten minutes which was plagued by stoppages in play.
Everton’s Leon Osman looked the most likely to score in the opening encounters, missing two chances inside 12 minutes after good work from Gareth Barry and Leighton Baines.
Palace had to wait until roughly the 20 minute mark for a decent effort on goal, when Yannick Bolasie fired wide from just outside the area following a scrambled attempt at a clearance from a Crystal Palace corner.
Both sides made changes in the second half with youngster Ross Barkley coming on for Everton and Cameron Jerome entering the game for Crystal Palace but it was all to no avail as neither side was able to break the deadlock.
Three points would have been handy for either team but the result means some stability for Palace while Everton have gained on Chelsea following defeat for the Blues at Stamford Bridge.