Fernandes capitalised on a poor clearance by Joao Palhinha to stroke a low finish into the bottom corner from the edge of the area in added time at Craven Cottage on Saturday.
United rebounded from back-to-back 3-0 losses to Manchester City and Newcastle over the past week that left Ten Hag facing his biggest crisis since taking over in the summer of 2022.
"With the goal, you could see the belief of everyone, fighting for that ball," Fernandes said but it was another tepid United display.
Scott McTominay thought he had ended United's scoreless streak when he tapped in Alejandro Garnacho's cut-back in the eighth minute but it was ruled out for offside against Harry Maguire.
Manchester City went back to the top of the table with a 6-1 win over Bournemouth.
City took off star striker Erling Haaland, who had a sore ankle, at halftime but still strolled to victory with goals from Jeremy Doku, Â Bernardo Silva (two), Manuel Akanji, Phil Foden and Nathan Ake.
A penalty in the 10th minute of stoppage time gave Sheffield United a 2-1 win over Wolverhampton Wanderers - their first league victory this season.
Oliver Norwood scored from the spot to spark wild scenes inside Bramall Lane, with his team having only picked up one point from its opening 10 games.
Cameron Archer opened the scoring for the hosts in the 72nd minute and Jean-Ricner Bellegarde equalised for Wolves in the 89th.
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