The defending champions, who had lost their first two games of the new season, have now bounced back with four consecutive wins to move up to second place.
Dilana Dilishati finished with a game-high 21 points. Zhang Dongxia registered a double-double of 10 points and 12 rebounds.
On the Shandong side, Yang Hengyu contributed 16 points, while Qiao Yanzi added 12.
"We've had an unbelievable group of players over the last two seasons and a squad of great people. I will miss them all hugely...I'd also like to say a massive thanks to the club for considering mine and my family's future and allowing me to make this move."
Jose Bordalas' men now travel to play Real Sociedad - one of the most attractive sides in La Liga, but who have struggled for form at home since the return of football in June.
It was immediately clear whether the pair would be replaced.
The previous best for the No.7 seed in Paris was the semifinals in 2012 when she lost to eventual champion Maria Sharapova 6-3, 6-3.
Hao joined Guangzhou Evergrande for study under world-class coach Marcello Lippi after managing the Chinese women's national team from 2012 to 2015. He was appointed the executive coach of the Chinese Olympic men's team, but his side failed in pursuit of a ticket to the Tokyo Olympics.
Newly promoted Elche and Huesca drew 0-0, although Huesca was the better side as Elche failed to get a shot on target.
As expected, head coach Gustavo Alfaro included Fenerbahce forward Enner Valencia and teenage Sporting Lisbon winger Gonzalo Plata in his 30-man squad.
"It's been long ride definitely. Everything came to my mind when I had my whole family, people who I loved to help me through the tough, tough time," said Kvitova. "I was just playing in the Philippe Chatrier, it was such nice to win the match and to be in the quarterfinal."