Steve Bruce's side occupy the relative safety of 11th spot but a run of three league defeats on the bounce, in which they have failed to score a single goal, has narrowed the gap between themselves and the bottom three.
Palace, meanwhile, have climbed the table to 16th and a home victory on Tuesday would underline the contrasting recent fortunes of the two sides.
And history on the hosts' side, too, with Hull having returned winless from their last 10 trips to Selhurst Park - a record stretching back to 1986.
Barry Bannan's late goal settled matters in this season's meeting at Hull, when the visitors finished with 10 men following Yannick Bolasie's dismissal.
That defeat will allow Tony Pulis' men to focus exclusively on the fight for top-flight survival as Palace seek to end their abysmal record of having been relegated from the Premier League on each occasion that they have competed in it.
Hull were beaten 1-0 at Norwich City, a defeat compounded by Tom Huddlestone's late red card, meaning he missed the trip to Roots Hall.
Much has been made of Palace's sizeable squad - described by one study as "the biggest in Europe" - and Pulis has relatively few injury concerns.
