Palace extended their run to seven matches in all competitions and the visiting Royals eight, as a lively match failed to produce a winner.
Noel Hunt hit the crossbar for Reading, Glenn Murray saw his effort for the hosts ruled out for offside and Kaspars Gorkss was denied a late winner by referee Andy Woolmer, as the two teams had to settle for a point apiece.
Jem Karacan saw an early shot saved by Julian Speroni in the Palace goal as the game got off to a frenetic start.
The home side quickly countered and Sean Scannell's effort at the end of a barnstorming run was blocked en route to goal, before Speroni was equal to a 30-yard thunderbolt from Reading centre-back Kaspars Gorkss.
The chances kept coming thick and fast. Jon Williams seized on Alex Pearce's defensive header to gallop through on goal, only for Royals stopper Adam Federici to smother the danger at the feet of the onrushing midfielder, and the Aussie keeper was soon in action again to stop a Wilfried Zaha attempt.
After a momentary pause in proceedings as a stray fox was ushered off the Selhurst Park pitch, Zaha fired narrowly wide from 20 yards before Speroni produced a superb reflex save to keep out Karacan's sizzling effort. Gorkss fired the rebound well wide.
Palace had the ball in the back of the net five minutes before the break, only to be denied by an offside flag.
Murray latched on to Williams' through-ball and beat Federici, only to see his celebrations cut short by a marginal decision by the assistant.
The game reached half-time goalless and Reading came out the stronger after the interval. A low Shaun Cummings centre was cleared to Jobi McAnuff, who blasted over from distance, before Speroni claimed possession at the feet of Le Fondre to prevent the frontman poking home.
And the Royals should have taken the lead just before the hour, but Hal Robson-Kanu could only nod McAnuff's terrific cross wide from close range when he should have hit the target.
With both sides struggling to create any significant openings, a moment of magic from Cummings almost handed the visitors the advantage.
Cummings eased past two defenders and set himself up with a good shooting opportunity, but could only fire a tame effort at Speroni.
After a period of Reading pressure Palace responded through Mile Jedinak, who forced Federici into a good save to deny his goalbound header.
But once again the away side replied, and went within inches of taking the lead. Jimmy Kebe centred for Noel Hunt, but the Irishman could only head against the crossbar with Speroni beaten.
The match's high drama lasted all the way to the final minute, with Karacan nodding a Palace effort off the line and Gorkss finding the back of the net with a header only for Woolmer to disallow the strike for an alleged push.
But in the end, there was no way through for either side.