As in the previous two rounds, Hingis and Vandeweghe did not have things all their own way, coming from a break down in the final set to see off their Chinese opponents, 6-4, 4-6, 6-2, in a little over two hours.
"It was an early break so we knew we had a whole set to play. Obviously after losing the second [set] it wasn't the greatest situation," Hingis said about their rousing finish. "I mean, they played really well in that first game too - they kept it away from me and made a lot of returns on CoCo's serve."
The No.6 seeds looked well set for a smooth passage into the quarterfinals when they took the first set and then moved 3-1 ahead in the second. "I think it was more frustrating to lose the second set because it was kind of there for us to take it," Hingis added. "But, I mean, this happens, and it's not a surprise for a tennis player to be broken in the first game after losing the momentum.
"But we were right back on it and I think that was the key; we broke them right back and then won a couple of tight games."
Vandeweghe is playing only her second event alongside Hingis - they teamed up to reach the final in Cincinnati - and admits the unison was not an expected one: "I got a call from and unusual number and the only reason I answered it - because I usually don't pick up numbers I don't know - was that it was such a bizarre number, plus whatever, so I knew it had to be some tennis player!
"I was just at home and Martina asked if I wanted to play Cincinnati and US Open. I told her that I already had two partners but let me think about it, and I almost felt a little big headed for telling her, 'Let me think about it'. I told my coach and he told me I was crazy to even think about it. I just enjoyed my time at home to let her sweat it out before calling back!"
Also advancing were a couple of more established pairs, including top seeds Caroline Garcia and Kristina Mladenovic, who had few problems defeating Eri Hozumi and Miyu Kato, 6-2, 6-3. No.5 seeds and recent Olympic champions Ekaterina Makarova and Elena Vesnina were made to work somewhat harder, fighting back to defeat Vania King and Monica Niculescu, 2-6, 6-1, 6-2.
Another team battling back from a slow start were wildcards Asia Muhammad and Taylor Townsend. Taking on No.3 seeds Timea babos and Yaroslava Shvedova, the young Americans looked well out of their depth for the opening 20 minutes only to produce a stunning turnaround to eventually triumph, 0-6, 6-4, 6-3.
The decisive moment came at 3-3 in the final set, Muhammad and Townsend harnessing the energy of a partisan crowd to break in a marathon game before repeating the trick a few games later to complete the unlikely upset. Their reward is a meeting with compatriot Bethanie Mattek-Sands and her partner Lucie Safarova, after they saw off No.8 seeds Julia Goerges and Karolina Pliskova, 2-6, 7-5, 6-3.