U.S. Open champion Stephens out-fought Halep to take the opening set and was a break up in the second but the world number one wound her way back into contention before running away with the deciding set.
When Halep served for the match at 5-1 with chants of "See-Mohh-Nahhh" reverberating around Court Philippe Chatrier, only a sudden attack of nerves could have denied her.
But when Stephens netted a forehand return on Halep's first match point, the Romanian could finally replace the bitter memories of her first three Grand Slam finals with one she will cherish for the rest of her life.
After consoling Stephens, she climbed into the stands to embrace Romania's former Olympic gymnastics champion Nadia Comaneci and 1978 Roland Garros winner Virginia Ruzici, the last Romanian to win a Grand Slam title.
There was also a big hug for coach Darren Cahill who was in the losers' box last year when Halep blew a commanding lead against Jelena Ostapenko in the final.
"Thanks guys it was amazing and I felt your support," Halep, who lost this year's Australian Open final to Caroline Wozniakci, said on court. "In the last game I couldn't breathe, I just didn't want to repeat what happened the other years."
Halep's win was one of the most popular for many years at Roland Garros and at times during the match the support for the 26-year-old was deafening.
That was not the case in the first though as Stephens, the first American not called Williams to reach the French Open final since Jennifer Capriati won in 2001, played flawlessly.
HIGH SHOT-COUNT
With both players boasting rock-solid defence and superb court coverage it was no surprise that the shot-count quickly rose in the baseline exchanges with Halep surviving a 25-stroke exchange to win her opening service game.
Stephens, moving silkily from side-to-side, out-Haleped Halep to move 4-1 in front, however, turning herself into a human backboard in some seemingly endless rallies.
Halep thought she had found a chink in the Stephens armour when the American served at 5-3 30-30 -- a huge roar from the crowd erupting as she won a drop shot duel near the net.
But 10th seed Stephens, cool as a cucumber, won the next three points to move ahead.
It looked bleak for Halep when she trailed 2-0 in the second set but the effects of Stephens' efforts suddenly caught up with her as the American began to wilt and Halep grabbed the momentum with nine consecutive points on the way to a 4-2 lead.
Halep then lost serve to love and when Stephens dragged it back to 4-4, it seemed Halep's revival might be over.
A crunching Halep backhand at 30-30 in the ninth game proved too much for Stephens as Halep crucially held and in the next game Stephens put a weary backhand wide to lose the set.
Halep turned the screws in the decider to grab a break and then another to lead 4-0 -- another explosion of noise greeting a sensational point in which Halep chased a drop shot down and was then equal to Stephens' attempted lob with a backhand smash.
One can only imagine what was going through Halep's mind serving at 5-1 but an ace steadied her nerves before she claimed her first Grand Slam at the 32nd attempt.
"Congratulations to Simona. There is no-one else I'd rather lose to than the number one in the world," a gracious Stephens, who will rise to four in the rankings, said.
(Editing by Pritha Sarkar and Christian Radnedge)
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