Benjamin Sesko came off the bench to score a 94th-minute winner as Manchester United survived a Fulham fightback to make it three wins in a row under Michael Carrick and move into the top four.
Fulham substitute Kevin followed up Raul Jimenez's late penalty with a super strike to level things up in added time but, in another classic under the new boss, Sesko struck as Carrick matched Ruben Amorim's longest Premier League winning streak at Man Utd in dramatic fashion.
After impressively beating Arsenal and Manchester City, Carrick's United passed another test that had its fair share of refereeing controversy.
The first incident came in the build-up to Man Utd's opener as they were initially awarded a penalty after Matheus Cunha was judged to have been brought down by Jorge Cuenca. However, after a VAR check, the decision was overturned, with Cuenca clearly winning the ball, although the hosts were given a free-kick for a shirt pull instead - much to Marco Silva's fury.
From the resulting free-kick, Casemiro headed home a Bruno Fernandes delivery for his fifth of the campaign. After announcing his departure at the end of the season, the midfielder is enjoying a farewell tour.
Cunha, who made a return to the starting line-up in the only change to the side in place of the injured Patrick Dorgu, thundered in to double Man Utd's advantage in the second half.
Fulham thought they had pulled one back when Cuenca tapped in a deflected Samuel Chukwueze shot that fell kindly into his path. However, after a VAR check that lasted around four minutes, the goal was ruled out for a marginal offside.
But after being brought down by Harry Maguire in the area, Jimenez scored from the spot, before Kevin's stunning equaliser looked like it had rescued a point for Marco Silva's side.
But Sesko, set up by Fernandes, had different ideas, thumping in his fifth goal of the season. A resurgent Man Utd are now five points off third place in the Premier League. Fulham drop to eighth.
Fulham boss Marco Silva expressed his frustration at Man Utd's opening goal after the game, suggesting he had been given different communication on the touchline about the decision.
"The game started with a horrendous, terrible decision from John Brooks with the penalty he gave," Silva told Your Site.
"A big, big mistake. It was the first time we had seen in the Premier League that the referee gave a penalty from a tackle and after the VAR came back with a free-kick.
"The communication I had on the touchline was that the penalty was given for the tackle and they came with a different foul after.
"Because the decision was so bad, they found a different foul like the pull."
Man Utd boss Michael Carrick was delighted his side successfully managed a different test after question marks were raised despite winning his first two games since returning as head coach.
"It's a special place this, and it does special things," Carrick said of Old Trafford while speaking to Your Site.
"And credit to the boys. We knew today was going to be a really tough game. Getting questions all week about breaking down a low block and beating teams that you should beat, and that was never the case today.
"Fulham are a really good team, and we knew that we were going to have a lot of questions to answer.
"Credit to the boys for the late goal last week that we conceded, then go again and win, and especially today, which was even tougher to take, probably to then find a winner for Benji.
"I'm just so delighted for him [Sesko], and he totally deserves it.
"It's a huge moment for all of us but for him especially, he deserves it. He's been fantastic since I came here. He will remember that feeling for quite some time."
