The reigning U.S. Open champion led by a set and break before Simona Halep managed to turn Saturday's final around with her relentless energy to win 3-6, 6-4, 6-1.
Despite the defeat, Stephens said she was glad Halep "finally got her light".
Halep had suffered plenty of pain in the past, losing three Slam finals prior to her victory on Saturday. It looks great on you.
As Stephen's level dropped, Halep demonstrated her mental strength, flipping the script from last year's final, when she led by a set and a break against Ostapenko before collapsing. "I don't get too up, too down", said Stephens.
Halep, the runner-up in 2014 and 2017, enjoyed a 6-1, 6-4 victory over 2016 champion and third seed Garbine Muguruza of Spain.
"I think it was the most important game of the match", said Halep.
Men's semifinals: No. 1 Rafael Nadal beat No. 5 Juan Martin del Potro 6-4, 6-1, 6-2.
Despite falling to the Romanian in Paris, Andrea Petkovic couldn't have been happier for Halep.
If Theim is going to earn the French Open title, he would be well-advised to win the first set.
Stephens played a first set of staggering quality, and not even the world number one, on her favourite court, could find the answers. Last season was one to forget and Halep became more determined to make up for the shortcomings and od much better in 2018.
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Halep said she has dreamt about winning Roland Garros since she was 14 years old.
A composed looking Stephens was indeed the first to break through, gaining a 3-1 advantage. The two traded games the remainder of the set, allowing Stephens to seal it on her serve in the 10th game.
Having changed her dress she came out fired up, and with Stephens's foot work becoming less neat she broke early, and then decisively again with a little help from the netcord, which seemed determined to help her to victory.
It was 5-0 by the time Muguruza eventually claimed a game.
Sloane Stephens of the US clenches her fist after defeating compatriot Madison Keys during in semifinal match of the French Open tennis tournament at the Roland Garros stadium, Thursday, June 7, 2018 in Paris.
Stephens, who has been serving well throughout the tournament, took the first game with a backhand victor. To Halep's dismay, she sent a backhand into the net. The final string snapped in the third set with Stephens trying to stave off a break point at 0-3.
Simona Halep and Sloane Stephens meet in the final of the 2018 tennis French Open.
Czech star Petra Kvitova added a message of her own.
'Congratulations on your first Slam.
The Brazilian was South America's most successful female tennis player, having won 19 major titles, including three Wimbledon singles titles and four United States championships.