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, it hit straight back as the much-maligned Sesko’s fourth goal in his last four games sealed Carrick’s third successive victory.