It's also a first for any Grand Slam tournament in the 50-year professional era.
Leading 5-4 and two points away from taking the first set at 0-30 on Hsieh's serve, Cibulkova struck a backhand onto the baseline that was called out.
Serena Williams has warned her Wimbledon rivals she is nowhere near her best despite powering into the quarter-finals without dropping a set.
Bertens, who was contemplating retirement a year ago after losing her enthusiasm for the sport, is the first Dutch woman to reach the Wimbledon quarter-finals since Michaella Krajicek in 2007.
"Today was tougher than the scoreline suggested".
But Pliskova, who reached number one in the rankings after Wimbledon past year, found some fight and capitalised on a loose game by Bertens that allowed her to break back and level the set at 4-4. So it's really cool.
Take off a week, then you start practising, then play a tournament.
Federer has now won 32 consecutive sets at Wimbledon to move within one straight-sets victory of breaking his previous longest streak at the All England Club, when he won 34 in a row between the third round in 2005 and the final in 2006.
Bertens hit seven aces and saved eight of the 10 break points she faced.
Men's fourth round: No. 1 Roger Federer beat No. 22 Adrian Mannarino 6-0, 7-5, 6-4; No. 2 Rafael Nadal beat Jiri Vesely 6-3, 6-3, 6-4; No. 8 Kevin Anderson beat Gael Monfils 7-6 (4), 7-6 (2), 5-7, 7-6 (4); No. 9 John Isner beat No. 31 Stefanos Tsitsipas 6-4, 7-6 (8), 7-6 (4); No. 12 Novak Djokovic beat Karen Khachanov 6-4, 6-2, 6-2.
Williams faces Camila Giorgi of Italy next, while 11th-seeded Angelique Kerber plays Daria Kasatkina of Russian Federation.
Dominika Cibulkova faces Jelena Ostapenko, Daria Kasatkina battles Angelique Kerber, and Kiki Bertens plays Julia Goerges in the other quarterfinal clashes.
The 2017 French Open victor stormed into the last eight for the first time at The All England Club with a 7-6 (7-4) 6-0 victory in the first of 16 fourth-round singles encounters on so-called Manic Monday at Wimbledon. He next faces Raonic, who defeated Mackenzie McDonald of the US 6-3, 6-4, 6-7 (5), 6-2.
Migrant kids to be reunited
Health and Human Services Secretary Alex Azar said Thursday there were "under 3,000" children separated from their parents. One child's status is unknown because the government lacks information about the parent, Fabian said.
IHOP to offer 60 cent pancakes for one day only
The restaurant revealed Monday it was going back to IHOP , just in time to promote a pancake deal tied to IHOP's 60 birthday. IHOP's "word of mouth" score skyrocketed following the name change, according to YouGov BrandIndex data .
Trump being sued for allegedly stiffing his ex-chauffeur
Due to the statute of limitations, Cintron is asking for just six years' worth of overtime wages ― a total of about 3,300 hours. He said he became part of Trump's security staff after the Secret Service took over driving responsibilities in 2016.