Bacsinszky has now made it to at least the quarter-finals at Roland Garros in three straight years, Sunday's 5-7 6-2 6-1 win particularly impressive given she threw away a 5-1 lead in the opening set.
But Muguruza felt it went too far, saying: "I think the audience was really tough today".
The Dane is a twice year-end world number one-ranked tennis player who has never won a grand slam.
Will turnabout be fair play for Mladenovic, when time comes?Add it all up, and it means that there will be a first-time major title victor at the end of the tournament. "That was a big thing on the match, but she managed to recover all those points", Muguruza said.
These two have split their only two meetings with Bacsinszky winning in this years Davis Cup and Mladenovic winning in the 2016 Eastbourne International. No one likes losing, let alone someone who has been as great a champion as she has, and especially not when this year's French Open draw is so wide open. I don't know how to explain.
"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".
Earlier, Rafael Nadal tied Roger Federer's record by reaching the French Open quarterfinals for the 11th time. Next up: Nadal vs.
Nadal continued his ruthless form by dispatching Spanish 17th seed Roberto Bautista Agut 6-1, 6-2, 6-2.
GETTYSerena Williams was in the stands to watch her sister in action
The only player to have beaten Nadal on clay this season is Austrian Dominic Thiem - who was playing Argentine Horacio Zeballos later Sunday in a fourth-round match.
Sania Mirza stormed into the quarterfinals of mixed doubles event as she and her partner Ivan Dodig of Croatia notched up a commanding 6-2, 6-4 win over Elina Svitolina (Ukraine) and Artem Sitak (New Zealand) second round match to book a last-eight spot.
Mladenovic often played to the fans, waving her arms to ask for more noise.
"They are excited, the atmosphere was just fantastic, it's not easy to handle for the both of us".
The spectators on the stands won't be so quick to turn on Mladenovic, just yet.
Mladenovic defended her support, saying: "I lost a final in Stuttgart against Laura Siegemund, a German player, and I thought the crowd was extremely tough there". "I think it's important that the three matches I have played have not been easy at all". "I experienced something in Germany where it was way more fired up, but I didn't criticise the crowd being unfair or anything, because it's also normal to see the crowd picking out their favourite". You give me the courage and strength to keep going in every point.
She is now hoping to get to the bottom of the problem before Wimbledon. 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. "I'd rather not say anything more".
Richard Gasquet retired from his all-French third-round match against Gael Monfils at Roland Garros after getting treatment on his right thigh.