Tauson, the last player to defeat US Open champion Emma Raducanu, had already knocked out Olympic silver medallist Marketa Vondrousova en route to the final before taking another big scalp in Sunday's showdown.
The defending champion from 2019, Ostapenko could not stop the 18-year-old Dane prevailing 6-3 4-6 6-4.
Tauson, who defeated Raducanu to win a Challenger event in Chicago prior to the final grand slam of the year in New York, where she was beaten by Ash Barty, struck eight aces and made just one double fault throughout the match.
Two breaks of serve saw her take the first set in just 30 minutes, though Ostapenko rallied in the second to force a decider.
However, the world number 70 had too much for her rival with the trophy on the line, immediately coming from a break down to haul herself level before breaking to take the match at the second opportunity.
Ostapenko was hunting a fifth career title, but the 2017 French Open champion has made it to just one other final in 2021, triumphing at Eastbourne prior to Wimbledon.