The Eagles dominated the first half against their London rivals and home keeper Rob Green made several fine stops, most notably from Wilfried Zaha.
West Ham improved after the break and substitute Sam Baldock had two late low strikes saved by keeper Julian Speroni.
Did you know?
West Ham had scored in their previous 10 league games before being held by Palace
But Palace, now unbeaten in five games, held on for a deserved draw.
West Ham undoubtedly had the edge after the interval and will feel they created enough opportunities to earn maximum points.
However Palace, who remain 17 points behind their London rivals, could have been three goals ahead by the end of the first period and the out-of-sorts hosts had Green to thank for keeping the scores level.
The England man made two blocked saves from long-range Chris Martin strikes and also a decent sprawling stop from a fierce Mile Jedinak effort.
But Green's best save saw him react brilliantly to tip over Zaha's deflected strike.
Palace played with a freedom and sharpness in the opening 45 minutes but the introduction of striker Carlton Cole lifted the Hammers.
Cole almost curled home the opening goal with a clever, placed finish after a Zaha mistake in midfield and Ricardo Vaz Te took a heavy first touch but failed to get shot away when played in by Cole.
As the home pressure began to mount, James Tomkins headed over and Palace keeper Speroni twice blocked Baldock shots with his feet at the near post.
But the Hammers could not find a way through a resolute Palace, whose best chance of the half saw Jermaine Easter blaze wastefully wide.
West Ham manager Sam Allardyce:
"As a manager you have to take it but one or two of the players in the dressing room were a little disappointed to get booed because we are at the top of the league (until Southampton beat Watford).
"You build up the expectation as we have done recently having done so well, and we didn't deliver today. But the fans have to stay with us and have to be patient, and then we'll all benefit in the end.
"It was not our best day but the last three games, playing with 10 men, caught up with the lads. I might have made a mistake picking the same team, but they had done so well. We livened it up in the second half but didn't hit the heights we know we can.
"We had probably the two best chances with Sam, but we couldn't convert them."
Crystal Palace manager Dougie Freedman:
"I'm pleased we could come to a big club like West Ham and force them to change shape and personnel.
"We had our chances, so did they. West Ham will always cause you problems but we stuck to our game plan and I felt a draw was pretty much a fair result.
"In my opinion West Ham will get promoted this season as champions."
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