World number one Halep made a slow start, misfiring on her first serve and spraying her groundstrokes wide early on in a duel that lasted more than two hours, before steadily wearing down her opponent.
Halep, meanwhile, has participated in a trio of major finals, losing each.
She won the US Open in September on a ranking of 83 and just 69 days after returning to the tour following her near year-long absence.
"Before, I gave it a lot of importance so that's why you're fighting every week, and I got there".
In the other men's quarter-final, number three Marin Cilic and number five Juan Martin del Potro were at 5-all in a first-set tie breaker when the match-up of past US Open champions was stopped.
With memories of their epic Australian Open semi-final in January - which Halep edged 9-7 in the third - still fresh in the minds they went to a decider.
"I have just to stay strong, to try to make her uncomfortable on court", Halep said, "and to try to play my game".
French Open 2018: Garbine Muguruza thrashes Maria Sharapova to reach semi-finals
Two women who have won the title at Roland Garros, Maria Sharapova and Garbine Muguruza , play each other in the quarterfinals. The victor earns a berth in the final at Roland Garros , plus the number one ranking that now belongs to Halep.
Both were appearing in the quarterfinals on the red clay of Paris for the first time, and both handled the occasion well. It is the first French Open semifinal between a pair of women from the United States since Serena Williams beat Jennifer Capriati on the way to the 2002 title. Particularly against Stosur and Sharapova, the 24-year-old was terrific and although she disagrees, Muguruza feels like the favourite coming into the semi-finals based on her clinical displays so far.
Halep raced into a 5-0 lead in the first set against misfiring 2016 champion Muguruza who had blasted Maria Sharapova off court on Wednesday for the loss of just three games.
French Open 2018 nearly presented the momentous occasion where the bitter rivals - Serena Williams and Maria Sharapova - former World Number ones, were about to clash in the 4th round.
Stephens's run to Saturday's final comes after a roller-coaster year since her US Open stunner.
Muguruza eventually got on the board and started to settle into the second set, breaking serve and getting to within two games of a decider at 4-2.
That set the stage for the lengthy ninth game where Halep stood firm.
This accuser is not after Weinsteins arrest & bail
The actress, Rose McGowan, who accused Mr Weinstein of rape, told the BBC it was an "amazing day for his survivors". The Associated Press does not identify alleged victims of sexual assaults without their consent.
But Muguruza was relentless and brought up two set points with a scorching backhand victor before sealing the opening set with a clubbing forehand that Sharapova fended into the net.
With Serena Williams still working her way back after giving birth previous year and withdrawing from the French Open in the fourth round due to a pectoral injury, Stephens is emerging as the face of women's tennis in the United States.
"She did a lot of things better than I did", Sharapova said.
"I lost three times until now and no one died", Halep said, "so it will be OK".
Stephens, who is now into the semi-finals of a major for the third time, leads Keys 2-0 in head-to-heads but they have never met on clay.
For more sports coverage, visit the ABS-CBN Sports website.
Grandma Unknowingly Smuggled Meth To Malaysia. She's Sentenced To Death
Exposto was handcuffed in court where she was consoled by her lawyers and Australian Embassy officials after the verdict. She was acquitted in December previous year of drug trafficking charges, however the prosecution appealed.