Dean Marney's late penalty rescued a point for Hull and increased the pressure on Palace boss Peter Taylor, whose team were booed off at the end.
Palace were poor but went ahead when James Scowcroft headed home David Martin's 81st-minute cross.
Hull were awarded a spot-kick in the last minute when Mark Hudson bundled over Michael Turner in the area.
Marney, who earlier hit the post with a long-range effort, smashed his penalty straight down the middle.
Crystal Palace manager Peter Taylor:
"The first half was totally unacceptable. We looked tired and people didn't want to try and get on the ball.
"We are a team playing with no confidence and we looked frightened.
"The players are under pressure but everyone's under pressure and we had to work hard to get a result."
Hull boss Phil Brown:
"The final-third quality is what has let us down and is what will separate us from being a middle-of-the-table team to a top-of-the-table team.
"That's why we brought Jay-Jay Okocha in but unfortunately he only lasted 15 minutes today.
"We gave him every opportunity because of the way he's been playing in the last four or five games, but he just couldn't stay on."
Crystal Palace: Speroni, Butterfield, Hudson, Cort, Craig, Soares, Watson (Green 62), Fletcher, Hughes (Martin 46), Scowcroft, Dickov (Morrison 62).
Subs Not Used: Flinders, Lawrence.
Goals: Scowcroft 81.
Hull: Myhill, Ricketts, Turner, Brown, Delaney, Garcia, Marney, Livermore, Pedersen, Okocha (Hughes 13), Windass (McPhee 67), Hughes (Featherstone 83).
Subs Not Used: Duke, Doyle.
Goals: Marney 90 pen.
Ref: Richard Beeby (Northamptonshire).