Nick Barmby's side have now kept 18 clean sheets in the Championship this season, more than any other team in the division.
And their defensive fortitude could yet earn them a place in the play-offs, from which they are separated by one point.
With Wilfried Zaha suspended, Palace, on a nine-game unbeaten run of their own, were lacking in creative spark but were always likely to find it difficult to break down the visitors' well-organised backline.
Corry Evans had an early sight of goal for Hull but dragged his shot narrowly wide from the edge of the box.
Anthony Gardner's smart block denied Josh King as he fired off a goal-bound effort from inside the box moments later.
The Tigers were not having it all their own way, however, and Palace's Chris Martin tested Vito Mannone with a stinging effort after 15 minutes.
Martin then attempted to turn provider as he whipped in a dangerous cross for Mile Jedinak but his header cleared the crossbar.
The home side forced a series of corners around the half-hour mark but Martin failed to find a team-mate with consecutive deliveries, James Chester and then King clearing to safety.
On the stroke of half-time Dougie Freedman's men had one more opportunity to threaten from a corner and though Martin picked out Jonathan Williams, the midfielder's shot was kept out by Mannone.
Barmby introduced Tom Cairney at the break as the largely anonymous Evans was withdrawn and the visitors were first to threaten in the second half.
Aaron Mclean forced a save from Julian Speroni with a 25-yard drive before Cairney announced his presence with a strike from even further out which was held by the Argentinian goalkeeper.
Glenn Murray went close to ending his 13-match run without a goal when his headed effort tested Mannone once more.
Freedman threw Sean Scannell into the mix with an hour gone and he went in search of his first goal since September but saw his shot from 20 yards fly just over.
Both sides had late half-chances to win it but Kyle De Silva pulled his effort wide and Robbie Brady's ambitious strike did not cause any major concern for Speroni.
The full-time whistle signalled a seventh draw in nine games for both clubs as Palace slipped into the bottom half of the table while City missed out on the opportunity to go fourth.