Stephens's run to Saturday's final comes after a roller-coaster year since her US Open stunner.
As Halep scurried to chase a shot that turned into a drop shot for Stephens and won the point for 4-0, her coach Darren Cahill leaped out of his chair and pumped his fist.
World No.1 Halep was defeated in the Roland-Garros final in 2014 and again a year ago but will have a chance of making it third time lucky in Paris when she faces Stephens on Court Philippe-Chatrier at 2pm.
Stephens applied a more patient strategy, Halep uncharacteristically insisted in applying a constant pressure towards her opponent's backhand. It started to pay a dividend and the Romanian forced a break point when Stephens served for the set.
Stephens wrapped up the set with a love hold and broke in the first game of the second as the errors continued to rack up for Keys, who surrendered her serve with a volley into the net.
Halep, owning a 6-5 record this season after losing the first set, struggled to find a way to change effectively her pattern. Halep took the trophy 3-6, 6-4, 6-1. After leveling the match at a set apiece, Halep looked sharper and more energetic in the first couple of games in the third set.
"I was very strong mentally to finish that", she said.More news: Happy election day, Timmins! Here's what you need to know to vote
This should be a great final as both players are playing well heading into the final.
The third set was a completely different story for Halep, who quickly built up a double break lead to get ahead 5-0.
A foot injury - and then surgery - had put her career on ice for 10 months and her ranking had nosedived to 323 in the world.
She said having to answer repeated questions about never having won a Grand Slam was "the toughest" and thanked her "really special" family and friends for giving her the strength to achieve her dream.
When asked about her previous Grand Slam final defeats, Halep told The New York Times: "I lost three times until now, and no one died, so it will be OK".
If Stephens holds her high ranking and can make her way to more Grand Slam finals this year and beyond, this sort of loss could prove beneficial to her long-term outlook. And, especially, as Halep collected game after game down the stretch. Halep fell to 0-3 with a trophy on the line at the Australian Open in January, beaten by Caroline Wozniacki.
He had threatened to stop working with her, saying that Halep's negative body language and attitude were standing in her way.
This time past year, Stephens was still sidelined with a foot injury that her walking around in crutches and Keys was coming off a second wrist surgery.