Eagles boss Roy Hodgson was back in the dugout after missing last weekend’s loss to Aston with Villa due to illness.
The evenly-matched contest saw Eberechi Eze fire just wide late in the first half, while the visitors were unable to capitalise on their best chance after the restart.
The result ensures the London rivals will share almost identical Premier League records for another week, with Palace only ahead on goal difference.
Sam Johnstone did well to parry away Andreas Pereira’s early effort from the left corner of the penalty area, later diving to deny Willian as the first period ticked past the 10-minute mark.
Fulham picked up two bookings in quick succession before Eze floated in a dangerous free-kick which the visitors were able to clear, and boss Marco Silva breathed a sigh of relief after Joao Palhinha was deemed fit to continue after knocking heads with Jordan Ayew in an aerial challenge – for which the Palace man was booked.
The hosts earned another free-kick and this time Eze aimed straight for the visiting net, where Bernd Leno was alert to grab the ball.
At the other end, Johnstone stooped to first collect Timothy Castagne’s close-range effort at his near post, then was called in to action soon after to turn away Raul Jimenez’s good opportunity to break the deadlock of an increasingly physical contest.
Eze looked to do the same when he patiently swerved his way through a cluster of white shirts, unleashing a strike that sailed just wide of the right post, while Leno picked Ayew’s cross out of the air to ensure it remained level at the break.
Will Hughes, who was involved throughout the first half, started off the second by forcing Leno into a simple save with an attempt from his preferred left foot.
Eze, who had just slipped a fine pass to the Odsonne Edouard, who was caught offside, then saw an effort of his own saved, while Jimenez could only nod Antonee Robinson’s cross wide of Johnstone’s right post.
The Cottagers should have taken the lead when Bobby De Cordova-Reid dispossessed Hughes in midfield and worked his way down the pitch.
The opportunity was wasted when the Jamaica international slipped in Jimenez, who overcooked his pass to the awaiting Pereira and the chance skipped past his foot.
Hodgson made a 70th-minute substitution, replacing Jeffrey Schlupp with Jean-Philippe Mateta, who has so far this season proven a productive partner with the in-form Edouard.
Joachim Andersen headed Eze’s corner over and Silva made his first change, swapping Pereira with Alex Iwobi and Fulham enjoyed one of their longest spells inside Palace’s final third, Willian forcing Johnstone into another good save with a sharp effort.
Palace had a late chance of their own through Mateta, who saw his weak left-footed shot stopped shortly before four minutes of stoppage time were added to the clock.
Hodgson elected to bring on 20-year-old Jesurun Rak-Sakyi for Edouard to see out the final few minutes, where Fulham staged a late rally but were not able to find the finishing touch.
