Federer, the Swiss world number two, plays Richard Gasquet in the last eight on Friday after Gasquet outlasted fellow Frenchman Gilles Simon in a marathon three-setter.
"I'm glad to reach the semi-finals in this tournament, but to be honest now, as I say always, health is the first of all of my life", Del Potro said.
"I like playing Gasquet on fast courts", Federer said afterward.
The victory ensured that the pair, who have won two Grand Slams and six titles together, qualified for the ATP World Tour Finals in London next month.
Fourth seed Cilic has reached the last four without dropping a set and overcame Nadal's countryman Albert Ramos-Vinolas 6-3 6-4, although the Spaniard did managed to break Cilic's serve for the first time in the competition at 3-3 in the second set.
"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".
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