The Blues were convincing 3-1 winners at Craven Cottage on Saturday thanks to a second-half Andre Schurrle hat trick, leaving the home side rooted to the foot of the table.
Despite Fulham being four points off safety going into the final 10 games of the top-flight campaign, Mourinho expects his German counterpart, who was appointed in February, to guide the club to safety.
"I think Magath is the man, a man with big experience, a man that has no fear of these big situations because he always has big situations," the Portuguese told reporters. "He has a lot to give to the players.
"I can imagine it is not easy. To go to a club mid-season is difficult. I would like him to survive and start a new season. For sure they will fight and get many points."
Fulham has not won in the Premier League since a 2-1 triumph over West Ham on January 1. After that victory over Sam Allardyce's side, the Cottagers have picked up just two points from a possible 24.
On Saturday the club travels to fellow fighter Cardiff City.