At least temporarily, Felix Magath's men could climb above the drop zone if they see off Steve Bruce's Tigers at Craven Cottage, with their rivals playing later.
Many had written off the Cottagers' chances of survival by the time that Felix Magath replaced Rene Meulensteen as manager but the German has led a revival at the west London club - with his side now sitting just two points adrift of safety.
Norwich City does not play not until later on Saturday and, with Cardiff City visiting Sunderland on Sunday, three points would lift the Londoners out of the relegation zone for the first time since January.
Fulham was rooted to the bottom of the top flight when Magath took over in February, with a 6-0 humiliation at the KC Stadium having been one of the low points of Meulensteen's short reign, but midfielder Scott Parker remains hopeful that his side can defy the odds and beat the drop.
"We all understand the responsibility we have as players," he told the club's official website. "Ultimately, we're going out there for a lot of people and it's in our hands to try and win games to keep us in the league so we all understand that responsibility that's needed from us.
"I'd probably be lying if I said the mood around the place was fantastic because obviously, when you're down near the bottom of the league, it's very tense, very nervy. I'm hoping we can all just stick together and give it one final push, and hopefully have a bit of luck, and see what happens."
Hull followed up its 5-3 FA Cup semifinal victory over Sheffield United with a 3-0 home defeat by Arsenal - the club's opponent in May's final - last time out in the league and will be keen to demonstrate that the players have not taken their eye off the ball.
The loss to the Gunners was the sixth in nine league matches for Steve Bruce's men and left the team six points clear of the relegation zone with a game in hand.
Victory for Hull on Saturday would represent a huge step towards ensuring that the team will play Premier League football for at least another season and Bruce wants to see his charges finish the job as soon as possible.
"We are still in a wonderful position, we've just got to see it through," Bruce told the Hull Daily Mail. "We've got three away games before our last home game. Against teams in and around us we've been particularly good and that's why we're in the position we're in.
"It would be nice to get a win to put it to bed but we've still got a bit of work to do."
Kieran Richardson (muscle), Mahamadou Diarra (knee) and Sascha Riether (illness) could all return for Fulham, while Sone Aluko (hamstring) and Shane Long (calf) are the biggest concerns for Hull.