Fernandes rescues Man Utd, Man City hit Bournemouth for six
Ten Hag's future at Old Trafford had come into question over the past week after consecutive 3-0 home defeats to City and Newcastle.
United were again far from spectacular at Craven Cottage but got a much-needed three points thanks to captain Fernandes.
The Portuguese midfielder has been a target of stinging criticism in recent weeks for not showing enough leadership on the field, but he produced a rare moment of quality when his side needed it.
Fernandes' 91st minute shot from the edge of the area had just too much power for Bernd Leno as it squirmed into the bottom corner.
"He showed every time as a captain he is an example," said Ten Hag. "You see today how he is working, how he is pressing and in the end he scored the goal."
Doku stars for City
City, by contrast, cruised to their three points but victory came at a cost for Pep Guardiola's men as Erling Haaland was substituted at half-time due to injury.
Jeremy Doku was the star of the show for the English champions as the Belgian winger opened the scoring and played a major role in four more goals.
Bournemouth held out for 30 minutes at the Etihad, but the floodgates opened once Doku prodded into the far corner after exchanging a one-two with Rodri.
Doku then teed up Bernardo Silva to slot home three minutes later.
Manuel Akanji was credited with City's third when Doku's shot hit the Swiss defender and flew past Andrei Radu in the Bournemouth goal.
Haaland was not moving freely for the closing stages of the first half and the Norwegian striker did not reappear for the second period.
His replacement Phil Foden got the fourth for Pep Guardiola's men courtesy of another Doku assist 25 minutes from time.
City were made to pay for a sloppy second-half performance when Luis Sinisterra pulled a goal back for Bournemouth.
But they still struck twice more as Silva scooped home his second of the game with an audacious finish before Nathan Ake crashed in a diving header.
Maupay breaks drought
Brentford edged the game of the day as the Bees came from behind to beat West Ham 3-2.
Neal Maupay ended a 45-game goal drought to put Brentford in front early on, but West Ham hit back to lead through Mohammed Kudus and Jarrod Bowen.
Konstantinos Mavropanos' own goal brought Thomas Frank's men level once more before Nathan Collins' towering header won the game 20 minutes from time.
Sheffield United secured their first win back in the Premier League in dramatic fashion as Oliver Norwood's 100th minute penalty beat Wolves 2-1.
All three goals came in the final 18 minutes. Cameron Archer fired the Blades in front before Jean-Ricner Bellegarde looked to have snatched a point for Wolves.
Victory is not enough to lift Sheffield United off the bottom of the table, but they move level on points with Burnley and within two points of safety.
Burnley became the first Premier League side to ever lose their first six home games of the season as Crystal Palace won 2-0 at Turf Moor thanks to goals from Jeffrey Schlupp and Tyrick Mitchell.
Everton were denied a third consecutive win for the first time since September 2021 as Ashley Young's late own goal rescued a 1-1 draw for Brighton at Goodison Park.
Third-placed Arsenal can move level with City at the top of the table should the Gunners win later away at Newcastle.
Tottenham, who began the weekend on top, are not in action until Monday when they host Chelsea.