Former world championship semi-finalist Fu, 44, had trailed 4-2 at one stage.
A second century of the match for Higgins put the 47-year-old Scot 5-4 up at the Hong Kong Coliseum. But Fu drew level with a break of 72 before his flawless final frame sent him through to face Ronnie O'Sullivan in Sunday's final.
The eight-player invitational event has seen record crowds this week and there were again more than 5,000 people to see the home