Shane Long stooped low to nod home with just three minutes of normal time remaining, after Nikica Jelavic had given the visitors hope of a point at Craven Cottage.
Ashkan Dejagah showed his quality to put Fulham ahead when he produced a wonderful shimmy and strike 10 minutes into the second half.
And Hull showed commendable spirit to claw level as Long scored to all-but secure their top-flight status and provide a confidence boost ahead of next month's FA Cup final.
After John Arne Riise and Hugo Rodallega went close for Fulham early on, Jelavic had Hull's first sight of goal - David Stockdale comfortably saving the Croat's close-range header - though the opening half-hour boasted few clear-cut chances.
However, Lee Mason waved away Hull appeals, before the second-half began with an explosive Rodallega volley he was unable to direct on target.
Riise and Lewis Holtby had been replaced by Dejagah and Kieran Richardson at the break, with Magath forced to make his third change just eight minutes into the second half.
Darren Bent replaced the injured Steve Sidwell in an attempt to offer Fulham some attacking impetus but it was Dejagah who opened the scoring with a curled effort that left Steve Harper with no chance.
While the Venezuelan may have been fortunate to be on the pitch, Hull could have no complaints with the quality of the goal - the former Athletic Bilbao man expertly guiding a precise Richardson cross past Harper.
However, it all went wrong for the home side from then on in as Riether's unfortunate attempted clearance was tipped onto his own crossbar by Stockdale before Jelavic tidied up the rebound.
With Hull piling on the pressure - Sone Aluko and Ahmed Elmohamady both hitting the woodwork - the visitors' late surge eventually proved too much for Fulham to hold back when Long headed home the equaliser.
A point makes life a little easier for Hull, who are edging closer to mathematical safety, though Magath's men remained mired in the relegation zone after a stunning collapse.
