Abdou Kadir Sabally gave Team Spurs the lead in the 55th minute of the match.
Fulham fought back and levelled matters through Buba Bojang in the 59th minute of the match.
This pushed the match into post-match penalty shootouts, which ended 4-2 in Team Spurs.
Team Spurs now joined Sea View, Nema City and Mariama Kunda in the semi-finals of the Sukuta nawettan league competition after winning their quarter-final match.