Hull have been slow starters on the road this season having conceded a league-high three goals before the 15th minute, and they were almost behind inside just three when Alex Iwobi’s deflected effort skimmed the roof of the net.
Fulham were clearly the better team in the first half, and Konstantinos Tzolakis spilt Oscar Bobb’s free-kick before the hosts eventually saw their pressure pay off.
Sander Berge laid the ball off to Iwobi on the edge of the box, and the Nigeria international shot first-time into the bottom corner to ease the tension in the stadium.
Tzolakis then stuck a leg out to deny Josh King from a tight angle, as Hull kept the deficit to just one heading into the second half.
Fulham have already dropped eight points from winning positions in the league this term, so were determined to score another and get themselves in a more comfortable position.
King should have done just that after he was played into a good position, but his shot was saved by Tzolakis’ leg again. Hull’s goalkeeper then made another decent stop as Iwobi poked towards goal from just a few yards out.
The Cottagers’ goalscorer was the standout player in the game, and he produced a delightful cross for Gonzalo Garcia, only for the striker to head onto the crossbar.
Fulham had conceded a joint-league high four goals after the 75th minute this campaign, so Arbeloa knew that despite Hull’s lack of threat going forward, his team were not home and dry yet.
However, if anyone was going to score again, it looked like it would be the hosts as they continued to drive forward, and given that Hull failed to register a shot on target, one goal was all the Cottagers needed to record a precious victory despite Ryan Sessegnon's late red card.
Fulham have now won five successive head-to-heads, while the Tigers are winless in their last five league matches after initially making a bright start to life back in the top flight.
Flashscore Man of the Match: Alex Iwobi (Fulham)
Catch up on all the match stats with Flashscore by clicking here