Jayden Bogle put the Blades ahead and although Harry Maguire equalised before half-time, Ben Brereton Diaz restored the visitors’ advantage soon after the interval.
Fernandes bailed out Ten Hag with a penalty equaliser before the Portugal midfielder’s long-range rocket put United in front with nine minutes left.
Rasmus Hojlund got United’s fourth to ensure they could finally enjoy a first league win in five games since beating Everton on March 9.
“I think we played quite well, also creating many more chances. Many positives. But also negatives. Conceding two goals from give-aways. It’s unacceptable,” Ten Hag said.
“I’m happy with the win overall. Have you seen some panic? No, not at all. We were very composed. We have to learn from this.”
It was a temporary reprieve for Ten Hag, who hopes to salvage sixth-placed United’s dismal season by winning the FA Cup and finishing high enough to qualify for the Europa League.
“We are striving to progress the team. The number of goals we are scoring in this moment is a huge progress. If we have our back four back together, then I’m sure we will be more consistent,” Ten Hag said.
The Blades are 10 points from safety with only four games left as they sink towards relegation just one year after promotion from the Championship.
Ten Hag endured stinging criticism after United stumbled into the FA Cup final with a spluttering win against second tier Coventry on Sunday.
United blew a three-goal lead in the last 19 minutes of normal time at Wembley and then barely survived a penalty shoot-out to book a final date with Manchester City.
Criticised for the sloppy performance, Ten Hag launched a strong defence of his credentials on Tuesday, telling journalists their negative coverage of the semi-final was a “disgrace” as the former Ajax boss insisted he has been successful for the last 10 years.
But United’s new technical director Jason Wilcox has reportedly been asked by co-owner Jim Ratcliffe to conduct an audit of Ten Hag’s training methods and sometimes fractious relationships with his players.
Flaws in defence
Watching from the directors box, Wilcox barely had time to settle into his seat before United’s Diogo Dalot had a fierce strike tipped over by keeper Wes Foderingham.
United were rocked in the 35th minute as Andre Onana gifted the visitors their opener.
Attempting to throw the ball to Dalot, the United keeper didn’t notice Bogle lurking in the way and the Blades midfielder intercepted before firing into the empty net.
Ten Hag stood ashen-faced on the touchline after the 75th goal conceded by United in all competitions this season — the club’s most in a single campaign since 1977-78.
United were behind for just seven minutes as Maguire stooped to head home from Alejandro Garnacho’s free-kick after a contentious foul on Kobbie Mainoo.
But the flaws in United’s creaky defence were exposed again in the 50th minute as they conceded two in a game for the fifth successive match.
Ben Osborn cut the ball back to Brereton Diaz and he punished sloppy marking to slot a cool finish past Onana.
Fernandes hauled United back on level terms with a 61st minute penalty after Maguire was dragged down.
To Ten Hag’s relief, Fernandes struck in the 81st minute, driving through midfield before unleashing a brilliant strike past Foderingham from 30 yards.
Four minutes later, Hojlund ended a run of eight games without a goal as he tapped in Fernandes’ cross to give Ten Hag some breathing space.
© Agence France-Presse
Photo: Twitter @B_Fernandes8