The American, however, relied on her perfectly-angled serve for a vital hold and took the set when the Frenchwoman scurried a forehand wide.
This was Muguruza's first attempt at defending a Grand Slam championship, and she ran into a determined Mladenovic, who was backed by a vocal crowd of countrymen who chanted her nickname, Kiki, throughout the match.
Asked again about the French crowd's behaviour, she said: "Let's say I understand".
"I just think that they were a little bit, sometimes should be a little bit more respectful". And each time, the less-accomplished player won.
It was the first time in the Open era that two Asian men had met as late as the third round in a Grand Slam tournament.
Bacsinszky delivered a terminal blow for the new guard when she downed 36-year-old Venus Williams 5-7 6-2 6-1. "Had also tough matches, which shows she's in a great rhythm".
Elsewhere, 19-year-old Latvian Jelena Ostapenko booked her spot in the next round at Roland Garros with a 6-1 6-4 victory over Lesia Tsurenko.
These two have split their only two meetings with Bacsinszky winning in this years Davis Cup and Mladenovic winning in the 2016 Eastbourne International. "That's the only important thing for me, no?"
"I was not thinking a lot because it's, you know, a lot of thinking in this tournament for me in the matches and stuff, so I try to go out there and block everything and just think about what I have to do to win".
Defending champions Novak Djokovic and Garbine Muguruza both play Sunday in the fourth round of the French Open, in a packed schedule created by multiple rain postponements. Next up: Nadal vs.
Jeremy Corbyn pledges to win hearts of Scottish left-wing voters
I was delighted, and humbled, to have the support of the community and be elected for a ninth time with a record number of votes . He said: "The people have spoken, and I have the same view now as I had after the European Union referendum vote".
The Canadian will now face the victor of the third-round match between Grigor Dimitrov and Pablo Carreno Busta. How right those folks were. "There was, like, few points that she played well at the end of the match, and kind of that was it".
"I'm still happy I'm here and playing".
Mladenovic said: "That was epic". I just think it's normal that it's such an awesome atmosphere. "I'll be honest there won't be 20 more".
The partisan crowd roared Mladenovic on to an upset victory, desperate to see a local win the women's singles for the first time since Mary Pierce achieved the feat in 2010.
Mladenovic, who has been hampered by back problems, leads the tournament in terms of double faults, having served 40 of them since it started. Sunday, June 4, 2017.
Garbine Muguruza of Spain reacts during the match against Kristina Mladenovic of France in their 4th round match at the French Open.
Momentum appears to be building for Williams as she attempts to win a title she came closest to lifting in 2002, when she was beaten in the final by her younger sister Serena.
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.
Bacsinszky is obviously the more experience player in these type of matches and has had to work less to get to this point.
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