Mourinho's men were convincing 3-1 winners at Craven Cottage on Saturday thanks to a second-half Andre Schurrle hat-trick, leaving the hosts rooted to the foot of the table.
With Fulham four points off safety going into the final 10 games of their top-flight campaign, Mourinho has backed his German counterpart, who was appointed in February, to guide them 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," Mourinho said of the former Stuttgart, Bayern Munich and Wolfsburg boss.
"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 have not won in the Premier League since their 2-1 success over West Ham on January 1.
After that victory over Sam Allardyce's side, Fulham have picked up just two points from a possible 24 ahead of Saturday's trip to Cardiff City.
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