Two goals from midfielder Ashkan Dejagah and defender Fernando Amorebieta inside three second-half minutes gave the Cottagers belief.
However, Nikica Jelavic set up an anxious finish when he nodded in with 15 minutes left before Hull snatched a late equaliser through Shane Long.
Saido Berahino's first-half goal, on 11 minutes, proved enough to give West Brom what could be a crucial victory in their own survival bid with a 1-0 win over West Ham at The Hawthorns.
The Baggies are five clear of trouble, on 36 points with three matches left, while West Ham sit 14th on 37 points with two games to play.
A superb 50-yard strike from Jonjo Shelvey helped Swansea beat Aston Villa 4-1 at the Liberty Stadium to close in on Premier League survival.
Tottenham recorded a 1-0 win at 10-man Stoke as they looked to make the most of Everton's defeat to Southampton in the battle for European places thanks to Danny Rose's first-half goal.
In yesterday's lunchtime kick-off, Everton saw their hopes of finishing in the Champions League places suffer a potentially fatal blow when they went down 2-0 at Southampton through a brace of own goals.
Antolin Alcaraz headed a cross from Rickie Lambert past Everton goalkeeper Tim Howard after just 54 seconds. It got worse for the Toffees - a point behind Arsenal, who host Newcastle tomorrow night - when Seamus Coleman also turned the ball into his own net.