Glenn Murray gave the visitors a third-minute lead with a volley before doubling their advantage 14 minutes later after linking up with Pascal Gross.
Calum Chambers pulled a goal back with a superb volley into the top-left corner on 47 minutes, before Mitrovic headed Fulham level just before the hour mark.
With both sides searching for a winning goal, Murray was denied by a fantastic Sergio Rico save before Mitrovic headed a Joe Bryan cross past Mat Ryan.
Luciano Vietto headed Ryan Babel's wayward shot into the net to complete the scoring 11 minutes from time.
The result means Fulham move to 17 points, five below 17th-placed Southampton, while Brighton remain 13th on 26 points.
Fulham: 2 Feb v Crystal Palace (A)
Brighton: 2 Feb v Watford (H)