It came on a rain-affected day in which neither of the scheduled men's quarter-finals came close to completion.

Halep has been a beaten finalist twice at Roland Garros and moved one win closer to an elusive first Grand Slam title.

She battled back to 5-5 from a double break down in the first set before losing the tie break, and then surged clear in the next two sets. 

"It's always a tough match when I play against her," Halep said.

"After the first set I just stayed strong and didn't give up.

"I missed a lot in the beginning. I tried to do too much. 

"I changed the tactics a bit and it worked."

Muguruza, the winner in 2016, thrashed Russia's Maria Sharapova 6-2, 6-1 today. 

An all-American semi-final is scheduled in the other half of the draw after Sloane Stephens and Madison Keys each enjoyed victories yesterday.

Top seed Rafael Nadal faces a battle on his hands to win an 11th French Open men's singles title after losing the first set 6-3 against Argentina's Diego Schwartzman.

The Spaniard leads 5-3 in the second set after recovering from a break down before a second rain delay proved decisive.

The match is due to resume at 12pm local time tomorrow.

Croatia's Marin Čilić is locked at 5-5 in a first set tie-break with another Argentinian in Juan Martin del Potro in the other match.

Austria's Dominic Thiem and unseeded Italian Marco Cecchinato - who stunned Serbia's Novak Djokovic yesterday - have already reached the semi-finals.