After 2 hours and 14 minutes, Halep rallied past the 12th-seeded Kerber 6-7 (2), 6-3, 6-2 and reached the French Open semifinals for the third time.
Halep went from out-of-sorts to on-target against Kerber, scrambling to every ball and staying the course to erase an early deficit.
"I never gave up". 'I think there is a lot of autobiographies out in the world, especially in the sporting world, that don't necessarily speak about whether they were rivals or someone they competed against.
Williams withdrew shortly before the match with a pectoral muscle injury, a moment Sharapova said she found briefly startling but not destabilizing. Muguruza is 3-0 in career grand slam semifinal matches.
The victor of Thursday's semi-final will also decide the world number one spot which Muguruza held for four weeks a year ago. Muguruza won 58 percent of her return points and broke six times in her quarterfinal victory.
Against Kerber, Halep stumbled out of the gate, dropping the first set in a tiebreaker. "Then I changed a little bit of tactics and it worked".
It is the first time that two American women have reached the last four at Roland Garros since 2002, when Serena Williams beat sister Venus in the final, after a semi-final win over Jennifer Capriati.More news: Basketball: Warriors ready for road test while Cavs confident in NBA Finals
Nadal was broken three times and lost the opening set of his quarterfinal Wednesday against 11th-seeded Diego Schwartzman of Argentina by a score of 6-4.
But he was 5-3 and 30-15 to the good when rain sent the players off for good. The 24-year-old Muguruza holds a 3-1 record over Halep, with the victor of the last-four clash to face either Sloane Stephens or her fellow American Madison Keys in the final.
"It's always a tough match when I play against her".
The second quarter-final between Marin Cilic and Juan Martin del Potro is also finely balanced with the players tied at 5-5 in the tiebreak in the opening set.
She missed several chances to go 4-1 ahead but she remained able to built the points more convincingly. Some of those matches were very defining for me.
Sharapova, back at the claycourt slam for the first time since 2015 following a doping-ban, walked on court with two French Open crowns to Muguruza's one and a 3-0 head-to-head record against the reigning Wimbledon champion.