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.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.