The 20-year-old from Guernsey looked to have thrown her way her chance of victory when, having served for the match at 5-3 in the second set, fell a break down and faced match point in the decider.
But she showed plenty of fighting spirit to break back before finally clinching a 7-5 5-7 7-6 (7/4) win in three hours 11 minutes.
Watson's win means she has followed in the footsteps of Sara Gomer, the last British winner of a singles title on the WTA Tour in California in 1988, and will move her back above compatriot Laura Robson in the world rankings, making her British number one again.
The success came just a month after Robson reached the final of a WTA event in China.
Sunday's final was a topsy-turvy encounter with both players carving out a total of 33 break points and breaking seven times each.
Watson took the first set by four breaks to three, but dropped her serve three times again in the second to let her 21-year-old opponent back into the match.
But after breaking Chang back to level the decider at 5-5, the Briton held her nerve in the tie-break to continue the rise of British women's tennis.
Watson could not hide her delight at the victory.
She said on the WTA Tour website: "I was in the changing room afterwards, changing my clothes, and I thought to myself, 'Did I really win?' So it's just starting to settle in.
"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, for moments like this.
"Britain has been breaking quite a few records recently, so I'm happy I could break another one today [Sunday]. I'm proud to do this for my country."
Chang served for the match at 5-4 in the final set, but, despite four match points, could not see off the battling Briton, who broke back before holding her nerve in the tie-break.
"She's an amazing returner, so I wanted to go for it," Watson added.
"What I've learned from my coaches is to go for it and not hope they miss. As you get better and play the top girls, you've got to go for it because they won't give it to you."
On the four match points she faced, Watson joked: "I was already thinking about how I was going to cry in the locker room.
"But after I saved the first one, I just took it point by point. I'm really proud of myself for getting through that."
Watson's win will also move her back above compatriot Laura Robson in the world rankings, making her British number one again.
Her success came just a month after Robson reached the final of a WTA event in China, the first time since Jo Durie at Newport in 1990 that had happened.
"Laura and I have come through the rankings together - juniors and seniors - and we're both very competitive, so when we see the other doing well, it pushes us," Watson added.
"Knowing Laura did so well in China a few weeks ago definitely motivated me this week. But I think it's great we're really good friends off the court as well."