He'll face 20th-seeded Pablo Carreno Busta in the last eight after the Spaniard knocked off fifth-seeded Milos Raonic 4-6, 7-6 (2), 6-7 (6), 6-4, 8-6.
Mladenovic next will face Bacsinszky, and Wozniacki meets Ostapenko.
With rain and storms forecast for later on Friday, Muguruza will be pleased to have booked her passage with the minimum of fuss, although if Mladenovic is her opponent in the fourth round she can expect an entirely different reception from the locals.
A year after showing so much resolve on her way to winning the tournament, Muguruza fell apart down the stretch as she became increasingly frustrated by the partisan crowd.
The 15th-seeded Monfils moved into the fourth round at the French Open for the seventh time.
The 24-year-old Mladenovic had never made it past the third round in Paris.
AB definitely due against India, says Miller
The Proteas were unchanged from the side that beat Sri Lanka by 96 runs in their Group B opener at the Oval on Saturday. They never allowed South Africa to settle once Imad trapped unsafe opener Hashim Amla leg before in the ninth over.
Mladenovic played her part in the noise, repeatedly shouting 'Forza!' [an Italian rallying cry] while she also revved the crowd up on multiple occasions.
But the Spaniard has been repeatedly answering questions recently about whether expectations are different now that she is a major champion and whether that sort of pressure might affect her on court.
She said in her post-match interview: "It's a match that was eagerly awaited by everyone, myself included". You give me the courage and strength to keep going in every point. And we're in the quarterfinals.
Pierce went on to lift the Suzanne Lenglen Cup in 2000, the last Frenchwoman to do so.
"I am in the fourth round of a Grand Slam for the first time".
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The UK and France are also to develop plans to create a new legal liability for tech companies which fail to take action against unacceptable content.
I like Mladenovic to advance to the French Open semifinal.
Wozniacki took the first set 6-2 but Bellis will resume at 5-2 up in the second on Saturday.
She compiled a whopping 46-15 advantage in winners against the 23rd-seeded Stosur, who won the 2011 U.S. Open.
Nishikori recovered to beat Hyeon Chung 7-5, 6-4, 6-7 (4), 0-6, 6-4; Monfils was leading 7-6 (5), 5-7, 4-3 against Richard Gasquet when his countryman retired after getting treatment on his right thigh. The Swiss needed just 68 minutes to seal the match.
Here are the results from the men's singles tournament at Stade Roland Garros on Sunday, June 4.
Mladenovic triumphed 6-1 3-6 6-3, but Muguruza appeared less than impressed by the behaviour of the crowd.
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Moreover, they have also not clashed in any semi-final match of an ICC ODI tournament . Amir was hit with injury in the practice session whilst he was bowling in the nets.