A point well earned from a second trip north in four days for the side as they battled back after seeing the home side create a number of chances before Palace themselves had some late opportunities to take all three points.
Jermaine Easter was the one change to the starting eleven that lost at Leeds at the weekend as he replaced the suspended Glenn Murray.
Robbie Brady created the first chance of the net as he played in the ball from the wing but no one was able to connect with the loose ball as it came across goal.
Sone Aluko should have opened the scoring when he got in behind the Palace defence and found himself in front of goal but Mile Jedinak cleared the danger.
The game was played in difficult conditions with rain sweeping across the stadium and the home side continued to create chances with a number falling to Robert Koren.
First he put a cross from Brady wide from 12 yards out and then he headed wide from a corner but he then got on the end of a deflected effort from Aluko but from just yards out put the ball over the bar.
The opening half continued at a fast pace and at the other end Wilfried Zaha saw his shot from the edge of the box blocked and then the home side thought they were set to take the lead with Stephen Quinn well placed but he put his volley just wide of the target.
It was Quinn who had the first opportunity of the second period when he made his way into the box and Julian Speroni did well to push the shot away and the rebound fell to Aluko but his effort was deflected out of play.
A couple of further chances were missed by the home side before a change was made from the bench as Aaron Wilbraham replaced Jermaine Easter.
Speroni was soon called upon again when he did well to deny Koren who had the ball come to him at the far post but the keeper saved well.
The visitors finished the game the stronger of the two sides with Zaha and Bolasie causing the home side problems. Zaha looked to be through on goal but was clipped by the last man and the defender was given a yellow as the striker looked to be away from him.
Bolasie nearly made the most of a poor back pass as he got to the ball but then put his effort just inches wide of the post.
In an all action finish both sides were going for the win and as Aaron McLean got the better of his man and got his shot in on goal Speroni produced an excellent save to deny the substitute.
In added time McLean saw a header saved by Speroni and Zaha produced some magic to beat a couple of defenders and get in space but his shot was saved by David Stockdale.
Palace could have snatched all three points at the death but the one sees another unbeaten run underway.
Hull City: David Stockdale, Paul McShane, James Chester, Alex Bruce, Robbie Brady (Liam Rosenior 84), Ahmed Elmohamady, David Meyler, Corry Evans, Stephen Quinn, Robert Koren (Nick Proschwitz 76), Sone Aluko (Aaron Mclean 76).
Subs Not Used: Eldin Jakupovic, Abdoulaye Faye, Paul McKenna, Jay Simpson.
Palace: Julian Speroni, Joel Ward, Jonathan Parr, Yannick Bolasie, Kagisho Dikgacoi, Owen Garvan, Mile Jedinak, Wilfried Zaha, Jermaine Easter (Aaron Wilbraham 61), Damien Delaney, Peter Ramage.
Subs Not Used: Lewis Price, Aaron Martin, Dean Moxey, Stuart O’Keefe, Kwesi Appiah, Danny Gabbidon.
Referee: Mr D. Drysdale. Attendance: 16,656.