The 20-year-old saved four match points in a match against Chang Kai-chen that she looked to have thrown away before claiming the 7-5 5-7 7-6 (7/4) win in three hours and 11 minutes.
The victory was Britain's first on the tour since Sara Gomer won in 1988, and Watson was overjoyed post-match.
"It's just starting to settle in," she said. "I've worked so hard for this moment my whole career. That's why I practised so hard, ran all those miles and lifted all those weights.
"Britain has been breaking a few records recently, so I'm happy I could break another one today. I'm proud to do this for my country."