Against the run of play, Jamie Scowcroft nodded Palace in front with nine minutes remaining, but Marney's spot-kick, with 30 seconds left of normal time, earned Hull a deserved point.
It was a poor performance from the home side and only Julian Speroni impressed. The Palace keeper made two stunning saves to stop Henrik Pedersen firing the Tigers side in front and suffered further frustration as Marney struck the foot of the post.
A goalless first half was a real let-off for Palace and Hull continued to make all the running after the break.
Dean Windass headed just over with Speroni off his line and substitute Bryan Hughes curled one from 20 yards which Speroni brilliantly tipped over.
For a brief few minutes Palace actually generated a few attacks as Boaz Myhill was forced to make two saves from Dave Martin and Tom Soares.
Mark Hudson also sent a header just over from close range.
With nine minutes left, Palace went in front when Soares burst through the heart of Hull's defence before passing to Martin on the left.
Martin's first-time cross was met by Scowcroft, who nodded down and into the far corner of the net.
But Hull kept plugging away and in the final minutes Michael Turner was up-ended just inside the box and from the penalty Marney struck low passed Speroni's outstretched right hand to earn Hull a point.