Fourth seed Del Potro's luck seemed to finally run out over on Hisense Arena.
The second set was tighter, with Del Potro having a break point in the sixth game.
Del Potro beat compatriot Leonardo Mayer in straight sets to reach the fourth round.
Mr del Potro, who comes from a rural area where the president was unpopular, declined.
Del Potro looked weary after his epic three-set semifinal win over Swede Robin Soderling the previous night.
It's an exhibition against Juan Martin del Potro, his first chance to compete at Madison Square Garden.
Del Potro's win, which took four hours and six minutes, ended Federer's five-year reign at the U.S. Open.
Cilic dropped the first set but took a 2-1 lead as Del Potro struggled to find his top form.
"I think Rafa deserved to win, " said del Potro, who has lost eight of his 11 matches with Nadal.
The Spaniard will face Juan Martin del Potro, who eliminated World No 1.
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"He's a big challenge for me also, " del Potro told reporters of Nadal.
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Del Potro reached the final at Indian Wells last week, but was unable to see off 89th ranked Kamke.
Rafael Nadal will play Juan Martin del Potro in the men's final Sunday.
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Argentine Del Potro beat Rafael Nadal 6-2 6-2 6-2 in the first semi-final.
Meanwhile at the World Tennis Tournament in Rotterdam, Juan Martin del Potro will face Julien Benneteau in Sunday's final.
Both men were in Montreal but fell at the quarter-final stage, Federer to Tsonga and Nadal to Del Potro.
Del Potro, 20, is currently seventh in the race to make the eight-man field for next month's Masters Cup.
Though Williams, Azarenka and del Potro were all in attendance, Nadal was the prime focus of the morning news conference.
Juan Martin del Potro can wrap up the tie if he beats Cilic in the first singles rubber on Sunday.
Second seed Juan Martin del Potro cruised into the semifinals with a victory in straight sets against Finland's Jarkko Nieminen.
It's always disappointing to lose a final. (In other finals) I lost five times to Djokovic, Federer, now Del Potro.
Del Potro had beaten third seed Murray and world No.1 Djokovic to reach the final, but conceded he couldn't match Nadal.
But mistakes at crucial times cost him dear and Del Potro's more consistent play brought him victory in two close sets.
I'm happy to get through to the second round and play Del Potro, I hope he's going to do well here.
Del Potro is scheduled to open the reverse singles on Sunday against Ferrer, depending on the seriousness of his thigh injury.
The day ended with an impressive performance from 18-year-old Argentine Juan Martin del Potro, who beat Swedish veteran Thomas Johansson 6-2 6-4.
Argentine Juan del Potro also won in four sets as he saw off Go Soeda 6-2 6-3 1-6 6-4 on Court 18.
Meanwhile in the other semifinal, Juan Martin del Potro made the perfect start for Argentina against the Czech Republic in Buenos Aires.
Del Potro broke Federer to level at 1-1 in the second, but the Swiss cruised to victory to the Basle crowd's delight.
Meanwhile, Juan Martin del Potro shocked World No.1 and home favorite Roger Federer in the final of the ATP tournament in Basel.
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