The 18-year-old looked set to lose in straight sets but saved five match points and then went 3-0 up in the decider only for world number 53 Hsieh to fight back and win 6-3 5-7 6-4 in hot and humid conditions in China.
Robson was not even born the last time Britain had a singles finalist - Jo Durie in 1990 - but Sara Gomer's reign as the last British winner in 1988 remains.
It has nevertheless been a brilliant week for Robson, who has built on her superb run to the fourth round of the US Open and will climb into the world's top 70 for the first time on Monday.
The British number one beat three top-50 players on her way to the final, and she made the perfect start with a break of serve in the third game, Hsieh struggling to deal with the teenager's power.
But the player from Chinese Taipei is a wily opponent and, with Robson struggling for consistency on her serve and forehand, Hsieh reeled off four games in a row and quickly wrapped up the set.
Robson was given some words of advice and encouragement from new coach Zeljko Krajan and responded by winning the first two games of the second set only for Hsieh to hit back with another run of four straight games.
Hsieh was reading her opponent's game extremely well now, offering the teenager very little pace and never the same ball twice, but Robson dug very deep to save five match points on her serve at 3-5.
That still left her opponent serving for the match but the teenager had a new confidence about her and she turned the tables to win three games in a row and level the match.
It was a crushing blow for Hsieh and another example of what makes Robson so exciting, and it got better for the Londoner as she made it seven straight games to move 3-0 up in the decider.
Hsieh was not finished, though, and for the third time in the match she put together a run of four straight games, and then added a fifth.
Robson again forced her to serve it out, but this time there was no twist, Hsieh clinching victory on her sixth match point when her opponent drilled a backhand wide after two hours and 47 minutes.
There was better news, though, in Tokyo, where British number two Heather Watson beat higher-ranked Czech Andrea Hlavackova to qualify for the main draw.
Robson had planned to play qualifying in Tokyo but missed out because of her performance in Guangzhou, so she will work for a few days with Krajan before attempting to qualify for the Premier event in Beijing next weekend.
The 18-year-old is predicted to climb to around 57 in the rankings on Monday, and she said on the BBC Sport website: "With a few more good wins I should be in the top 50 so I've got to keep working hard.
"I think I'm playing pretty well, I feel confident at the moment even though I lost today. I've got qualifiers in Beijing and it's going to be tough there as it is one of the top tournaments of the year.
"It will be good to get a few more days of practice in before Beijing, work on the things that didn't go to plan in the final in Guangzhou and hopefully I can do well in Beijing."