Fulham's Luciano Vietto fired wide from close range in the first minute as the hosts started brightly.
But the visitors went ahead on 14 minutes when Pogba linked up with Martial and lashed in a powerful shot from a tight angle, beating Sergio Rico at his near post.
Nine minutes later it was two, when Martial ran from inside his own half and finished beyond Rico.
Pogba’s penalty sealed the win with 25 minutes left after Maxime Le Marchand brought down Juan Mata.
Victory continues Ole Gunnar Solskjaer's unbeaten record as caretaker manager and puts Man Utd in fourth, one point above Chelsea.
Fulham stay 19th on 17 points.