The visitors came alive in the second, creating multiple chances to leave Selhurst Park with all three points after there was nothing to choose between the teams in a first half devoid of entertainment.
Josh Maja curled narrowly wide from the edge of the penalty area, forcing Vicente Guaita into a one-handed save, with a close-range header from Ivan Cavaleiro’s delivery.
Ruben Loftus-Cheek came close with a powerful effort that went just wide of Guaita’s left-hand post and Joachim Andersen’s header was saved.
Palace had just three attempts as an attacking power, failing to test Fulham Alphonse Areola.
The draw lifts Scott Parker’s Cottagers to 23 points – three behind 17th-placed Newcastle – while the Eagles are 10 points above the relegation zone in 13th.
Crystal Palace – Fulham 0:0