The Eagles, who had won their previous three home games to boost their hopes of beating the drop, were by far the more adventurous side.
But they fluffed their lines in front of goal with James Vaughan and Pablo Counago squandering chances to put them ahead.
Hull offered little in response, although they will be satisfied at stretching their unbeaten run on the road to six games.
Their cause was not helped by injuries to Richard Garcia and Anthony Gerrard, who both had to be replaced during a pedestrian first half.
Palace's first shot on target did not materialise until the 33rd minute when Counago's curler was saved by Vito Mannone
But the Eagles finished the opening period well on top and Vaughan, playing the final game of his three-month loan spell from Everton, should have put them ahead in the 41st minute.
Counago robbed Paul McShane on the halfway line and charged forward before sliding the ball into Vaughan, but the striker scuffed his shot horribly wide.
Two minutes later Neil Danns wriggled into the area and teed up Counago but his goalbound shot from six yards out was bravely blocked by Kamil Zayatte.
Iin first-half stoppage time, Danns was felled on the edge of the area and Vaughan curled the free-kick just over the crossbar.
Vaughan limped out of the action shortly after the restart but Palace continued to press and midfielder Alassane N'Diaye was inches away from breaking the deadlock with a curling shot from 20 yards.
Counago prodded a decent opportunity wide and N'Diaye blasted over from the angle when a cross looked by far the better option.
A strong burst forward from right-back Nathanial Clyne had Hull back-pedalling furiously and his ball set up N'Diaye again but Mannone beat the Frenchman's shot away.
Palace hearts were in their mouths as the final whistle approached when Hull won a corner which was floated in by Robert Koren and just missed the head of Kevin Kilbane in front of goal.
But there was still time for the Eagles to try to grab a winner, and in the final minute Danns was denied by another last-ditch block from Andy Dawson and Counago blasted the rebound over the crossbar.
Crystal Palace: Speroni, Clyne, Davis, McCarthy, Wright, Danns, Garvan, N'Diaye, Zaha, Counago, Vaughan. Unused substitutes: Price, Barrett, Dorman, Scannell, Bennett, O'Keefe, Obika.
Hull City: Mannone, Rosenior, Zayatte, Gerrard, Dawson, Ashbee, Koren, Harper, Stewart, Garcia, Barmby. Unused substitutes: Duke, McShane, Kilbane, Bostock, Cullen, Simpson, Solano.
Referee: Steve Tanner (Somerset).
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