The 20-year-old Ostapenko, who had never won a Tour-level title before, clawed back from a set and 3-0 down to storm past the experienced Romanian in a two-hour long contest on Court Philippe Chatrier.
Latvia's Ostapenko strung together four games, finding her targets with excellent winners time and time again, and she claimed the second set with a forehand that flew past Halep.
She turned 20 during the tournament and was still a teenager when she lost the first set of her first-round match against Louisa Chirico of the United States.
So if Jelena Ostapenko catches fire and starts blasting winners - as we know the youngster can do - will Halep panic?
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. "There are no words". Though Simona Halep was expecte to win and was the favourite, she did manage to win the first set easily by 4-6.
After losing the opening set 4-6, Ostapenko was 3-0 down before an astonishing turnaround saw her come through to win the second and third sets 6-4, 6-3.
"I fought for every point and I'm glad it finished my way".
Perhaps not a typical 20-year-old, she revealed a passion for ballroom dancing - she was professional for seven years and it's something she believes helps her footwork - and Agatha Christie's detective novels, sometimes reading to pass the time during tournaments. Three years ago, it was something new, but now I know.
"I would like to win all of the Grand Slams". So I want to really hit the ball (smiling).' About her popularity in Latvia, Ostapenko said: 'My match they were translating in the city center on big screen. 'I think so, because I always had the possibility I could hit the ball really hard. "I'm so happy, thank you guys".
"I would like to win all of the Grand Slams". I think I played okay.
"I have faith that eventually she will get over it".
"It's a tough moment for me, but it's gonna go away, I hope, with time", Halep added.
"I am sick in the stomach with emotions but hopefully I can win this one in the future", said Halep.
Simona Halep's coach Darren Cahill, about Ostapenko.
- She guided a lovely forehand down to line to draw level with her 36th victor of the match.