Hong Kong's Fu denied Melbourne-born Robertson a home victory by getting the better of an exciting final to take the $70,000 top prize.
World number one Robertson had been looking to fulfil one of his career ambitions by winning a tournament in his homeland, but fell just short and also missed out on becoming the first player to win back-to-back ranking titles in the same season since Ronnie O'Sullivan in 2003, having won last month's Wuxi Classic.
World number 18 Fu, age 35, had an excellent 2012/13 season, highlighted by a run to the final of the German Masters in February, and has carried his momentum into the current season to land a coveted ranking crown.
After turning pro in 1998, Fu quickly established himself as one to watch by reaching the final of the Grand Prix in the same year, losing to Stephen Lee. Arguably since then he has not won the titles his talent deserves, mainly because he has struggled with his technique for long periods of his career.
His first ranking title came at the 2007 Grand Prix and he also won the Premier League in 2003. Fu's snooker CV would have been more impressive but for a couple of agonising defeats in the two biggest ranking events as he lost 10-9 to Shaun Murphy in the 2008 UK Championship final and 17-16 to Peter Ebdon in the World Championship semis in 2006. He was also runner-up to Ding Junhui at the Masters two years ago.
But today's victory is a huge step forward for Fu and he can now set his sights on regaining a top 16 place and winning more titles. He and wife Shirley had their first child, a girl called Alicia, last December, so perhaps fatherhood has given him a new perspective on snooker which has helped his results on the table.
A high quality start to the final saw the first four frames shared, Fu making breaks of 98 and 80 while Robertson compiled 78 and 92.
Fu then took three of the next four to lead 5-3 after the first session. Robertson won the ninth with a 57 and made 60 in the next, only for Fu to clear with 58 for 6-4. The Asian ace added a 70 in frame 11 to extend his lead.
Robertson made 59 in winning the next and got the better of a scrappy 13th to close to 7-6. But Fu won the 14th on the colours and finished in style with the highest break of the match, 102.
"I had a good season last year and played some good snooker, but it was frustrating not to win a title," said Fu. "This takes a lot of pressure off me and I can enjoy the rest of the season. The standard is so high now that it's just very nice to be able to win a tournament.
"Neil and I played the best snooker throughout the week, although today it didn't really happen for us. We both got a bit tired towards the end, and twitchy here and there. It's very tough against Neil because he's world number one and even though he wasn't at his best he played some good safety. I'm just very pleased that I made a good break in the end to win. There was so much drama throughout the whole match, a lot of frames could have gone either way.
"It was just nice to be able to participate in the final here, playing in Australia is great. Thanks to the fans for their support and I hope we can come back next year. "
Robertson said: "I'm very pleased to have got to the final, but the semi-final against Mark Selby which finished last night took a lot out of me and I didn't really get going today.
"Every credit to Marco for the way he played, his safety was brilliant and he didn't allow me to get any flow going.
"I kept a positive frame of mind tonight but I was always playing catch-up. Marco has been the best player this week and deserved to win today.
"My game has come a long way over the last couple of years in terms of consistency. I'm disappointed not to win today but hopefully the tournament is here to stay."
