Playing her first final of 2019, Ostapenko settled well enough thereafter but Gauff looked imperious, shrugging off a double fault at the start of the ninth game to take the set.
Gauff converted her third break-point chance for a 2-1 lead. "Linz is my special place".
After taking the historic moment, Gauff said: 'I want to thank God for always supporting me like I wouldn't be here without him.
Gauff, who fell in the second round of Upper Austria Ladies Linz qualifying, gained entry into the main draw due to a withdrawal and has made a resounding run this week.
Tennis.com adds that Gauff will rise from her current WTA ranking of 110 to 80 or 81 for her appearance in the final, but could climb as high as 71 if she wins the competition.
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"This kind of proves I'm able to hang in on this level and I'm really proud of myself today".
"This is insane", Gauff added after winning in 92 minutes.
The youngest-ever victor of a WTA Tour title was two-time US Open champion Tracy Austin, aged just 14, at Portland in 1977. "Obviously a lot of players play for the grand slams and want to win slams but I think this is a good stepping stone in the right direction".
Ostapenko finally got a look at her opponent's serve in set two as they exchanged breaks early on, before the weight of what she seemed set to accomplish appeared to hinder Gauff.
The American fought through in the final game to serve out victory, staving off three break points and coming through on her second match point.
"First time in my life, even in juniors, that I got into something as a lucky loser and now I'm in the final", said Gauff.