United came into the Craven Cottage clash under a cloud after the midweek Carabao Cup defeat at home to Newcastle.
They were quiet for long periods of the game but a moment of brilliance from skipper Fernandes, who came in for criticism from former United players after the Newcastle loss, gave manager Erik ten Hag a welcome three points.
Fernandes evaded attempts to close him down on the edge of the penalty area before placing his shot beyond Fulham keeper Bernd Leno.
United thought they had taken a 1-0 lead after eight minutes but VAR ruled out Scott McTominay’s effort for offside.
The Scot tapped in Alejandro Garnacho’s cut back but referee John Brooks overturned the goal after VAR ruled Harry Maguire had interfered with play from an offside position.
The decision was a wake-up call for the hosts who were looking to build on Wednesday’s last-16 3-1 Carabao Cup victory at Ipswich.
Craven Cottage was fired up and Willian dragged the Cottagers up the pitch with a slaloming run but his effort was blocked at the last moment.
The Brazilian was Fulham’s main creative outlet in the final third and in the 27th minute he produced a delightful cross, but, in keeping with Fulham’s season so far, no striker was there to finish at the back post.
Nigeria international Alex Iwobi marauded from his own half into United’s box but was wasteful in front of goal, failing to hit the target.
The hangover from United’s back-to-back 3-0 home defeats against Manchester City and Newcastle was clear to see as ten Hag’s side lacked intensity, with Fernandes’ skewed added time cross summing up their first-half efforts.
The visitors searched for a way into the game after halftime through Garnacho who enjoyed touches in promising areas before a dangerous cross was tipped over by Leno.
The Cottagers also came close from the following set-piece when last week’s goal scorer Joao Palhinha failed to keep his effort down as Onana made another save to maintain the deadlock.
The minutes ebbed away and substitutions from both sides sapped the games’ intensity before Fernandes’ free-kick in the 83rd minute gave United hope late on.
The Portuguese midfielder had not been heavily involved but showed what he is capable of when he struck a dipped free-kick towards Leno’s bottom corner and the Fulham keeper did well to prevent United edging in front.
But there was no denying Fernandes in added time. He combined with Rasmus Hojlund and jinked inside onto his preferred right foot before unleashing a powerful shot that proved too much for Leno, who could only palm it into his bottom corner.