In a clash between two bottom-half sides with comfortable cushions over the relegation places, Oliver Glasner's men were well on top in the early exchanges, but they could not convert their first-half dominance into goals.
The Eagles were briefly punished when an improved Fulham broke the deadlock through Rodrigo Muniz, but Jeffrey Schlupp's late thunderbolt ensured a share of the spoils in the capital, keeping the Cottagers 13th and Palace 14th, three points below their hosts.
Fulham now have another London derby away to Brentford on next Saturday's menu, two days before Palace host Manchester United at Selhurst Park.
Palace fail to make most of early domination
Despite losing Eberechi Eze to a knee injury sustained against Newcastle, Palace welcome the equally effervescent Michael Olise back to the first XI in his place, while Fulham were without Tosin Adarabioyo following reports that he has decided to leave the club at the end of his contract this summer.
Palace jewel Olise should have given the Eagles their reward for a lightning-quick start in the sixth minute, finding himself one-on-one with Bernd Leno, but the winger's right-footed strike sailed wide.
The visitors' pressure remained unrelenting, but a brief stoppage for an injury to Leno disrupted their momentum, and Fulham - who also came close through a 43rd-minute Issa Diop header which flew over the top - got to half time with their clean sheet intact.
Despite being second best for most of the first half, Marco Silva's troops benefitted from Palace profligacy, and Muniz needed just one opportunity to give the Cottagers an arguably undeserved lead in the 52nd minute.
Schlupp produces magical moment for Palace
Tyrick Mitchell was the guilty party, playing a lackadaisical pass straight to a white shirt, and a slick passing move ended with Muniz nonchalantly heading home from Timothy Castagne's delivery into the six-yard box.
A second could and perhaps should have arrived for the hosts in the 64th minute, but Bobby Decordova-Reid's back-post finish was poor and trickled wide from Andreas Pereira's pass.
There would be no goal for the hitherto red-hot Jean-Philippe Mateta, but his replacement Odsonne Edouard almost did what his colleague could not within just a few seconds of coming on, testing the gloves of Leno with 20 minutes of normal time remaining.
Eventually, Palace's pressure would pay dividends with three minutes of normal time remaining, as Adam Wharton fizzed a pass into the feet of Schlupp, who took one touch before unleashing a 25-yard rocket off the bar and in.