The Argentina defender fired the only goal of the Premier League game in the closing stages, via a deflection off Fulham's Sasa Lukic, as United followed up their midweek Europa League win against Rangers with three points.
It was only Ruben Amorim's fourth victory in 12 Premier League matches since taking charge of United.
And the back-to-back wins have come since Amorim declared last weekend his team was "the worst, maybe, in the history of Manchester United."
It was another blunt attacking display from United, who managed just one shot on target, but the valuable three points moved the Red Devils above Crystal Palace and up to 12th.
United forward Rasmus Hojlund endured another ineffective match and was replaced by Joshua Zirkzee after 58 minutes, with Amorim's side appearing to require more inspiration from skipper Fernandes to find a breakthrough.
Fulham, who saw Joachim Andersen's late header superbly cleared off the goal-line by United substitute Toby Collyer, have won one of their last five league games and sit 10th.
Earlier, Leicester gave their hopes of avoiding relegation a major boost - and piled the pressure on Tottenham coach Ange Postecoglou - by fighting back to win 2-1 in the capital.
Brazil forward Richarlison opened the scoring for Spurs in the first half, but Jamie Vardy and Bilal El Khannouss struck for the Foxes in the space of four minutes straight after the restart to halt their side's seven-game losing league run.
Ange Postecoglou reacts after Bilal El Khannouss scored Leicester City's second goal. (AP PHOTO)
Tottenham, who squandered a host of chances as they chased an equaliser, have won only one of their last 11 league matches and sit 15th in the table.
West Ham defender Emerson's second-half header earned Graham Potter's side a 1-1 draw at Aston Villa.
Jacob Ramsey fired Villa into an early lead and, after the Hammers struck a post through Carlos Soler's effort, Emerson's header got the visitors back on level terms midway through the second half.
Villa had earlier been dealt a blow when England defender Tyrone Mings left the pitch in tears before half-time after sustaining a knee injury - less than three months after returning from anterior cruciate ligament surgery.
Brentford secured just their second league win on the road this season as they beat London rivals Crystal Palace 2-1 at Selhurst Park.
Bryan Mbeumo gave Palace a second-half lead with a retaken penalty after Maxence Lacroix's foul on Nathan Collins.
Mbeumo's initial spot-kick hit a post, but Palace skipper Marc Guehi was adjudged by VAR to have encroached in the area.
Kevin Schade headed the Bees into a 2-0 lead and, although former Millwall forward Romain Esse pulled one back on his Palace debut, the visitors held on for their second victory in 10 league matches.
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