The 44-year-old's feat drew a roar of approval at the Hong Kong Coliseum, which has seen record crowds of more than 5,000 throughout the tournament.
It continued a remarkable resurgence for Fu, who underwent eye surgery in 2017 then spent almost two years off the tour due to the Covid-19 pandemic.
"It is amazing," Fu told World Snooker Tour. "I can't believe what just happened there.
"This is my best moment so far as a professional. To do something like that in front of my home crowd - we have had huge attendances so far this week and it is the best thing I have ever achieved."
A three-time ranking tournament winner and former World Championship semi-finalist, Fu had beaten Mark Selby 5-2 in the opening round of the eight-player invitational event.
Higgins started with a century and also led 3-1 and 4-2 before Fu clawed his way back to parity by winning the eighth frame.
A second century took the Scot one frame from victory but Fu levelled with a break of 72 before holding his nerve to wrap up his victory in style.
Fu will meet Ronnie O'Sullivan in Sunday's final after the world champion launched a superb comeback to beat Neil Robertson 6-4.
Australian Robertson made three centuries as he raced into a 4-1 lead but O'Sullivan responded with two tons and a 93 as he reeled off five straight frames.