Halep was a set and a break down in the final, but went on to win 3-6 6-4 6-1 at Roland Garros.
The 26-year-old had failed to win all three of her previous Grand Slam finals, and she admitted on Saturday that another defeat in the final seemed likely when Stephens was ahead in the tie.
"I felt 'it's gone, it's not going to happen again, but it's OK. I have just to play'," Halep told reporters.
"When I started to win games, I said that last year the same thing happened to me. So I said there is a chance to come back and win it. I believed in that, and my game was more relaxed. I could make more things on court, and that's why I could win.
"It's a special moment. I was dreaming for this moment since I started to play tennis. Roland Garros is my favourite Grand Slam. I always said that if I'm going to win one, I want it to be here."
The world number one is 11th in the all-time rankings of the Women's Tennis Association.