The Blues 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.
Despite Fulham being four points off safety going into the final 10 games of their top-flight campaign, Mourinho expects his German counterpart, who was appointed in February, to guide them to safety.
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"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 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 they travel to fellow strugglers Cardiff City.