The No. 20 seed prevailed against Safarova in a matchup of two of the women's tour's top servers.
The numbers were becoming simpler: No4 seed Elina Svitolina had to reach the semi-finals to have a chance at No1. Brady would hold serve in that fifth game, but Pliskova would rattle off the next eight games after that to complete the rout and advance to the final eight. The two players had taken part in the final of this event in 2009. If they got that far, it was victor takes all: the No1 ranking. Vandeweghe has the type of game that could test Pliskova and she thrives in the gritty Flushing Meadows atmosphere.
In the match, Pliskova hit 23 winners and committed just nine unforced errors. Del Potro had won his only major title in his career and had put an end to a series of five titles, Federer in NY.
And Keys joins Sloane Stephens, Venus Williams and Vandeweghe in the quarterfinals. Brady is ranked 91st in the world but that will improve when new rankings are issued next week. She beat Andrea Petkovic, No23 seed Barbora Strycova, and Monica Niculescu, the last of them in a final-set tie-breaker. Definitely she can play better than she was playing today.
"I think it's great" to have such numbers, Coco Vandeweghe said, "in our American Grand Slam". "I think sometimes I play good shots, good rallies, and then there are hundreds of mistakes and not a good shot". The third round saw Pliskova on the verge of defeat as she had to save a match point against Shuai Zhang (26 WTA).
Sam Querrey was nervous about playing a late-night match at Ashe on Sunday but his jitters didn't last.
Pliskova broke immediately, broke again for 4-0, and nearly did so in the fifth game, too. If she fails to do so, Garbine Muguruza will rise to No 1 for the first time. I think it will be an easier match to the tune of 6-2 6-4. But was now in to the first quarter-final at her home Major.
Should Pliskova reach the final in NY she will retain the world number one ranking, but a first grand slam title would be even greater reward for the 25-year-old.
The 32-year-old Kanepi, a former world No 15 whose career was nearly ended by illness and a crippling injury to both feet, will face either fourth seed Elina Svitolina or Madison Keys for a place in the semi-finals.
Jennifer Brady's tournament ended Monday with a 6-1, 6-0 loss to Pliskova, but the former UCLA Bruin found positives in reaching the fourth round of a Grand Slam for the second time this year.
It was not a given Nadal would win after having lost twice in three of their previous meetings, but he never gave the unseeded Dolgopolov a chance, breaking serve six times in the 1 hour 41 minute match.