The visitors started the strongest in the first half, as Alex Iwobi wasted two early opportunities to give his side the lead, flashing both efforts wide after some lovely link-up play from Rodrigo Muniz.
The Brazilian has four goals in his last three games, and almost added another to his tally as Andre Onana was forced into a decent save, before Sasa Lukic could only chest wide from close range.
United really struggled in the opening 25 minutes, but Alejandro Garnacho sparked them back to life when his sumptuous effort was brilliantly cleared off the line by Antonee Robinson.
Diogo Dalot then struck the outside of the post, but Fulham still threatened down the other end, as Muniz also hit the post just moments later on the counterattack.
Andreas Pereira and Garnacho then forced saves from Onana and Bernd Leno respectively, in a lively half that had everything but a goal.
The second half was a lot quieter, but the breakthrough came from Fulham on 65 minutes, as Calvin Bassey lashed home his first goal for the club after the ball fell kindly in the box from a Pereira corner.
Bruno Fernandes then had a chance to salvage an equaliser for the hosts, but Leno saved his shot well as the crowd roared Erik ten Hag’s side on.
Marcus Rashford was also denied by Leno late on, before Fulham had a chance to double their advantage when Harry Wilson’s thunderous strike from distance whizzed just past the post.
Maguire should have done better with a close-range header which flew just over the bar, but just as the Cottagers thought they held on for a remarkable victory, which would have been their first at Old Trafford in 17 attempts, the Englishman netted in the last minute of normal time to salvage what looked like a point for United.
However, deep into stoppage time, Iwobi was put through on goal and slotted cooly past Onana to earn all three points on a dramatic afternoon in Manchester.
The result means Marco Silva’s team record their first PL away victory since August, while defeat is a huge blow to United’s hopes of finishing in the UEFA Champions League places for next season, with Ten Hag having a lot to ponder.
Flashscore Man of the Match: Alex Iwobi (Fulham)
