Timeless rival Federer was even faster, dismissing Ukrainian qualifier Alexandr Dolgopolov 6-4, 6-2 in 61 minutes.
Federer next faces Richard Gasquet, who outlasted fellow Frenchman Gilles Simon 7-5, 6-7 (5), 6-3.
"I saw his frustration, for sure", del Potro said. "I think both of us, we played at a very high level of tennis".
"I have a tough match against Grigor and know I will have to play my best. but I am playing well".
The result sees the World No. 1 move into the semi-finals of the Shanghai Masters where he will face 4th seed Marin Cilic.
Boris Johnson hits out at 'so-called friends and allies'
That's fewer than the 48 needed to trigger a leadership battle, so if May is determined to stay, she can - for now. Today, May said that the "ball was in EU's court" as the next round of Brexit negotiations got underway.
Sixth seed Grigor Dimitrov, who saved match points on Wednesday against Ryan Harrison, had a more comfortable day as he beat American 10th seed Sam Querrey 6-3 7-6 (7-3).
The 16-times grand slam victor, who beat Dimitrov in three sets in the China Open semi-finals last week, fired 32 winners and won two crucial breaks to prevail in two and a half hours at the Qi Zhong Centre.
"A lot of matches in a row winning and very happy with everything, let's see what happens tomorrow, but being able to win in Beijing and now semifinals here. tough events against tough players".
The German prodigy and the 29-year-old, whose career has been beset by injury, went toe to toe in the second set and the tie break was just as tight until Del Potro grabbed the crucial mini-break.
A relieved Nadal looked up to the heavens and raised his arms at the end.
The world No.2 broke Gasquet at 5-5 to gain the advantage and went on to take the first set.