Del Potro beat Nadal in the 2009 semifinals at Flushing Meadows, then ended Federer's five-year championship reign by upsetting him in the final.
But it didn't halt his assault as he capped a 6-4 6-2 7-5 victory.
Nadal has won a record 10 French Opens, two Wimbledons, two U.S. Opens and an Australian Open title.
Blue skies and bright sunshine greeted fans at the U.S. Open on Monday, where world number one Rafa Nadal and third seed Roger Federer were scheduled to play under an open roof at Arthur Ashe Stadium.
ESPN.com noted it was the first time in Federer's career his first two matches at a Grand Slam event went to a decisive fifth set.
As Rublev pondered a first Slam quarterfinal, the women's draw saw Estonia's world number 418 Kanepi book her place in the last eight of a major for the sixth time. He pushed it to 5-5 by holding serve for much of the set, but just like the first, all it took was one break from the five-time U.S. Open champion to clinch the set.
The U.S. Open runner-up past year, Pliskova advanced to face either No. 20 CoCo Vandeweghe or unseeded Lucie Safarova.
Vandeweghe echoed Williams' comments from after her quarterfinal victory, thinking back to the last generation of American women that, along with Venus and Serena Williams, included Lindsay Davenport and Jennifer Capriati.
Pliskova raced to a 4-0 lead in the fourth-round match and closed the set in just 26 minutes after Brady double-faulted on set point.
With the match on serve at 2-1 to the German in the second set, the razor sharp Federer tore through six successive games to take the set and 1-0 lead in the third. But one of those defeats came in five sets in the 2009 final at Flushing Meadows, when del Potro won his only Grand Slam title and ended Federer's streak of five consecutive championships in NY.
Monday's match represented more head-to-head dominance for the 19-time major victor, who has never lost in his career against Kohlschreiber. The top-seeded Nadal faces Alexandr Dolgopolov on Monday afternoon.
Thiem, who was forced to quit with an injury against del Potro at the same stage in 2016, celebrated his 24th birthday on Sunday.