From then on, Halep looked resigned to her fate and Ostapenko held her serve easily before breaking again, firing a stunning backhand victor on the return - her 54th victor in all - to clinch the victory of her life.
"Serena was always, like, kind of my idol, because I really enjoyed watching her", said Ostapenko after becoming the first unseeded victor in Paris since 1933.
"I'm really happy to win here", Ostapenko said after the match, evidently under the huge influence of emotions, "I think I still can not believe it because it was my dream and now it came true".
The Latvian moved level on serve when Halep hooked a forehand wide and then earned another break to chalk up a fourth game on the trot.
"I slept very well [last night]".
"I felt a little bit nervous", said Ostapenko, according to ESPN. I was close, but again, I lost it.
Ostapenko had blasted her way into the final on the back of 245 winners - more than any other player in the draw, man or woman. And she had come back from the brink against Elena Svitolina in the quarter-final, and survived an onslaught from Karolina Pliskova in the semis to enter her second Major final.
"Of course I would like to win all of the grand slams".
Ostapenko held a 40-0 advantage on the Halep serve but couldn't break, was broken in the ensuing game after holding game point and lost the next game after it went to deuce. There was grace in that brutal hitting, and the steady footwork which is its foundation is a legacy of her balance and quick feet in the ballroom. I fought for every point. "She deserved to win", said the Romanina.
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But she admitted: "It's a tough moment for me, but it's gonna go away, I hope, with time".
'I think when I go back home there will be a lot of attention and this is really nice because I made history for my country, ' said said. Halep, beaten by Maria Sharapova in the final here in 2014, had been the favourite from the start pf the tournament and looked to be cruising at a set and 3-0, with points for 4-0.
Ostapenko suspected that Saturday's match in sunny, warm conditions in Paris was shown on a big screen in the city center in Riga, Latvia's capital city. You wouldn't want to miss this spectacle.
If Ostapenko, who is a former junior Wimbledon title, can maintain this kind of form, then she may just take some stopping when she gets to the All England Club in three weeks' time. To play final, it's an awesome thing. [But] I'm really powerful and I was just born with that power probably. "So if I can reduce them, I think will be helpful".
"She played really well, all the credit". With Wimbledon just around the corner, starting July 3, her sudden appearance on the scene makes things more interesting.
"Hurts a lot, and I need time just to - I don't know. At some point I was like a spectator on court", she said.
As for Halep, she knows this loss will be painful for a while and admits she needs time to get over it. Rafael Nadal spent the second week of last year's Roland Garros on a boat with his girlfriend, trying to forget the agony of injury that forced him to withdraw from the tournament after the second round.
Next on the agenda for Ostapenko is the Aegon Classic in Birmingham but she is not yet in the field, now still one out with the rankings cut-off several weeks ago, although a wild card will surely be made available if she chooses to take it.
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