The Slovakian won 6-4 6-1, but the match will be remembered for a ludicrous umpiring decision at a crucial stage of a tight opening set.
Hsieh, who stunned world number one Simona Halep on Saturday, was the victim of a glaring mistake by umpire Zhang Juan.
As Hsieh served at 4-5 0-30, Cibulková pummeled a return deep into court and immediately challenged the linesman’s call of out, prompting Hawkeye to show it had indeed been in.
That was when common sense deserted the court.
The umpire awarded the point to Cibulková, even though Hsieh had actually scrambled her return back.
Hsieh argued, correctly, that the point should be replayed, but the umpire would not budge, saying she could not remember if Hsieh’s shot had gone in.
Cibulková could have intervened but simply stood on the baseline in the advantage court as if to prepare for a 0-40 situation, even with the crowd chanting “replay the point…replay the point”.
When a referee was summoned, Cibulková was called to the net, and after further dialogue was told the point would be replayed. Her indignant response hardly endeared her to the crowd who understandably had taken Hsieh’s side.
When play resumed Hsieh battled back to 30-30, but Cibulková won the game to take the first set, and she powered through the second to book a last-eight clash with fellow power-merchant Jeļena Ostapenko of Latvia.
Thirty-third ranked Cibulková, who has responded in feisty fashion to being bumped out of the seedings by Serena Williams’ elevation to 25th, fought her corner in a news conference.
“I don’t want to talk about it because I would get really upset and angry about that, because it was ridiculous what happened there,” Cibulková said.
“It never happened to me in my career that the umpire changed the decision. It was really ridiculous for me.”
Asked whether she had sympathy for Hsieh, Cibulková was adamant it was not the Taiwanese player who had been wronged.
“The right decision was, of course, to keep the decision,” the 29-year-old said.
“This happened to me so many times that I had exact the same point, and the point was given to the other player. I had no sympathy because it’s just about the chair umpire.”
Hsieh, 32, did not speak until after playing doubles later but was more gracious.
“I understand, she’s a fighter,” when asked if Cibulková had shown a lack of sportsmanship. “She fights for every point.”
Of the umpire, she added: “Maybe she’s tired and she doesn’t see the ball. It’s quite common, even players on the court sometimes get tired and don’t see something, it’s normal.”