Carrick revels in 'best feeling' after Man Utd leave it late
United took the lead through Casemiro's first half header and looked in command when Matheus Cunha netted after the interval at Old Trafford.
In an incredible finale, Raul Jimenez's penalty with five minutes left gave Fulham hope before Kevin's wonder-goal hauled the visitors level in stoppage-time.
To United's immense credit, they hit straight back as the much-maligned Sesko's fourth goal in his last four games sealed Carrick's third successive victory.
After masterminding surprise wins over Manchester City and Premier League leaders Arsenal, this remarkable encounter suggested former United midfielder Carrick might have the Midas touch.
Unbeaten in their last seven league matches, United moved up to fourth place as their bid to qualify for next season's Champions League gathers pace.
"It's the best feeling I have to say," Carrick said. "Some of the best moments I've been part of here, you can dissect performances and there are plusses and not, and then you get a moment of elation and excitement like that.
"For me there's no better place than in front of the Stretford End like that. It ends up meaning more.
"People leave here with more than just, 'United won today', it's layers on top of that, the emotion and the feeling and it's why we all love it so much."
United needed the dramatic contribution from substitute Sesko after letting Fulham off the hook
Carrick conceded that was a sign there is much to work on despite the turnaround since he took charge.
"The character we showed after a big setback, a huge setback, in the 90th minute, to do that coming off what we did last week is probably the most pleasing thing. To keep the belief, to keep the confidence," he said.
"We can play better and that's probably the most pleasing thing. The rest of the game, we can play better, we can do a lot of things better in certain moments but I can't fault the players' belief.
"It's taken us through today and it's a good feeling when it does."