The 10-time champion lost the first set 6-4 to the impressive Argentine Wednesday, but returned under sunny skies Thursday to win the next three sets 6-3 6-2 6-2 to reach the French Open semifinals.
Nadal, the undisputed king of clay, had lost his first set at Roland Garros since 2015 and was a break down in the second, but he regrouped during a 53-minute delay.
The Argentinian took the second of them and served out for a 7-6 (7/5) 5-7 6-3 7-5 victory in just under four hours.
He eventually lost the set and found himself trailing 3-1 in the third set before turning things around, with Cilic largely undone by his 74 unforced errors.
Del Potro has served 53 aces to reach the semi-final and his forehand, a stroke that could chop down trees, worries the very best as he showed by beating Roger Federer at last year's U.S. Open and winning the Indian Wells title in March. I was close to quit this sport.
No player in history has won as many grand slam titles at a single tournament as Nadal has in Paris.
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'It has been a long time without a good feeling on my body.
And yet, insists Nadal: "I just go on court knowing that every match is hard, and I can lose and I can win". Although Del Potro has beaten Nadal five times, Nadal won their last encounter and leads 9-5 overall head-to-head.
Soderling made the final as well the following year when Nadal gained revenge to claim a fifth French Open.
"I don't give much attention to those studies".
"I don't know if I will win, but I will take a big love from you", an emotional del Potro, whose career has been hampered by injuries, told fans during his postmatch interview. After that, Simona Halep plays Garbine Muguruza: the victor will be world No. 1.
"I played again one of my best matches on clay", Halep said after coming back from a break down in the second set. I was able to open the court on his forehand.
Nadal was serving at 5-3, 30-15 after having dropped the first set when play was stopped. "Rafa will go big into that backhand and although that part of Del Potro's game has improved in the past year, he's not going to hurt Rafa from that wing".