The Spaniard, 31, had sealed the year-end number one spot for a fourth time on Wednesday, but he was made to work hard by an enterprising Cuevas.
Nadal is looking for his maiden title on the Bercy hard courts, which would take him clear of Novak Djokovic with a record 31st Masters triumph.
The 16-time Grand Slam champion will take on world number 77 Filip Krajinovic in the quarters, after the Serb beat Nicolas Mahut 6-2, 3-6, 6-1.
"It's normal that at the end of the season after all the things that happened... All the matches I played with high intensity, it's normal that there are body issues a little bit.
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"So it's nothing strange. Something that's completely normal and accepted."
Nadal started far stronger than he did in Wednesday's win over Hyeon Chung, breaking early on thanks to a couple of trademark forehands.
Cuevas played his part during the first set in front of a near-capacity crowd, hitting an outrageous 'hot-dog' shot between his legs for an outright winner.
The reigning French and US Open champion has only won two of his 75 ATP titles indoors, with just one at this level coming at the 2005 Madrid Masters.
He broke in the third game of the second set, only to hand Cuevas a lifeline with a string of uncharacteristic unforced errors as the world number 36 hit straight back.
The South American forced a tie-break, but after Nadal had moved 4-2 in front, the top seed dumped two volleys into the net and Cuevas levelled the match at the first opportunity.
Cuevas also had to call the trainer after appearing to dislocate his thumb when sliding for the ball, but he grabbed the break back as Nadal struggled to put the match to bed.
That proved to be the unseeded player's final show of resistance, though, as his illustrious opponent reeled off three successive games before wrapping up the match with a big serve out wide.
- Del Potro one win from London -
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Argentina's Juan Martin del Potro closed in on a place for the World Tour Finals after beating Robin Haase 7-5, 6-4.
He will face ninth seed John Isner in the last eight after the American beat Grigor Dimitrov 7-6 (12/10), 5-7, 7-6 (7/3).
Last year's runner-up Isner will qualify for the Tour Finals if he wins the tournament in Paris.
"It's going to be a good battle next round trying to qualify for London," said Del Potro.
"But anyways, I think I have two ways to take, one is London, one is my home and vacation."
Belgian David Goffin sealed the penultimate Tour Finals spot despite slumping to a 6-3, 6-3 defeat by journeyman Frenchman Julien Benneteau.
Lucas Pouille's slim chances of reaching London ended, though, as the home player lost 7-6 (8/6), 6-3 to the big- serving Jack Sock.
The American will next face veteran Spaniard Fernando Verdasco, who knocked out Austrian fifth seed Dominic Thiem with a 6-4, 6-4 victory to reach his first Masters quarter- final since 2012.