The 15-year-old, who burst onto the global scene at Wimbledon as the youngest qualifier in the tournament's history and then made a run to the last 16, will now move way inside the top 100 in the world rankings.
It was a nervy end for Gauff, understandable given her lack of experience at this level, as she was broken to love with the match beckoning, but a pep talk from her coach Corey, who also happens to be her father, calmed her mindand she broke back to take the title in one hour and 40 minutes.
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Gauff started confidently, having come into the tournament as a lucky loser but then put together a string of victories that included beating world No 8 and top seed Kiki Bertens in straight sets.
Ostapenko, after failing to capitalise on break points in the opening game of the match, struggled to find her rhythm and was too easy to read, allowing Gauff to move into a 3-0 lead.
The Latvian never threatened her opponent's serve again in the opening set as the younger woman took the opening set of her first ever WTA Tour final.
But Ostapenko, who has dropped from 22 in the world to 72 in 2019, hit her straps in the second set and started to play the kind of tennis that won her a French Open title two years ago.
When her coach Marion Bartoli came onto court before the decider, she told her charge that the teenager across the net, who was broken three times in a row in the second set, was getting tired and would get even more fatigued.
But it proved to be far from the truth as Gauff broke for the third time in the match for a 2-0 lead, Ostapenko apparently losing concentration when the umpire awarded her opponent the point instead of replaying it when Hawkeye proved the line-judge's call to be incorrect.
Gauff then compounded the break, aided by some weak serving and a double-fault that was barely halfway up the net, and produced two emphatic serves and a stare down the court to suggest to Ostapenko that this match was well and truly over.
There were some nerves evident when she had her first match point on the Ostapenko serve, flying a forehand well long, and the 22-year-old forced her opponent to serve it out.
It was never going to be easy and Gauff did double-fault immediately before losing her serve, told by her coach and father that they were going to walk, not run, to the finish line.
Walk she did, with head held high, and her third match point was more than enough invitation, going toe-to-toe with Ostapenko from the baseline and winning, in such a modern way, with a challenge.
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