After the Spaniard had raced into a 5-1 lead in the third set there was a loud and sympathetic cheer from the crowd when Rublev held his serve in the following game.
Del Potro appeared set for a last-16 exit in NY as the sixth-seeded Thiem raced through the opening two sets in 73 minutes. Fellow American Madison Keys grabbed the last four games to eliminate fourth seed Elina Svitolina 7-6 (7-2) 1-6 6-4 meaning there four USA women are in the last eight for the first time in 15 years after Venus Williams and Sloane Stephens had previously advanced.
Del Potro famously ended Federer's five-year reign in 2009, also ultimately denying Federer a non-calendar-year grand slam, before a chronic wrist injury nearly ended his career. On match point, Rublev hit a harmless backhand into the net.
As if that weren't impressive enough, he didn't even face a break point throughout the match and took advantage of his chances by winning four break points of his own.
Del Potro is not the player he was eight years, but the power in his groundstrokes remains there and his spirit remains as dogged as ever, as Thiem will attest.
Pliskova will next face either 37th-ranked compatriot Lucie Safarova or USA 20th seed CoCo Vandeweghe for a place in the semi-finals. As Thiem's energy rose; del Potro seemed to start succumbing to the viral illness that plagued him the first two sets of the match.
When it was over, del Potro raised both arms overhead and threw his head back, enjoying the fans' adulation, then crossed himself.
Coming off the back of a superhuman effort to beat Dominic Thiem over five sets, Del Potro was the clear underdog coming into the match. "I don't know why".More news: France Says North Korea Close to Long-Range Missile Capability
The bottom half of the draw will feature two interesting encounters as Pablo Carreno-Busta will take on Diego Schwartzman, while Sam Querrey will face Kevin Anderson.
Play on the featured court will then wrap up with a match between women's fourth seed Elina Svitolina and 15th seed Madison Keys. He was impressive, however, in his straight-sets victory over Serbia's Dusan Lajovic in the first round.
He led 30-0 but lost his focus and scooped a forehand long to allow Del Potro back in the contest.
The 5th set started off routinely with both players displaying power and consistency and both holding easily to get to 2-2.
In the resulting tiebreak, Thiem suffered a meltdown and Del Potro levelled with a gravity-defying crosscourt forehand victor.
But Nadal went back to work on Labor Day in the round of 16 and was his ruthless best again as he demolished the always risky and acrobatic Alexander Dogopolov 6-2, 6-4, 6-1.
The "Dominator" was in full control, dictating the play with deep forehands, and he sealed the set with a cracking backhand victor down the line. It was an extraordinary effort considering that del Potro has also been suffering from a virus this week. We could even hear it on center court. Thiem then drew the return error from Del Potro to give him game point for 5 all, but Del Potro answered with a down the line forehand clean victor to bring about deuce. This picture could be might awkward in the near future, depending on the result of their match. Juan Martin del Potro prevented it once and can do it again.