The world number one, Rafael Nadal remains on course to win the Paris Masters and started the tournament as the favourite.
But Cuevas proved a tricky opponent, especially with his monster serve and gritty rallying.
Cuevas, like Nadal, is best on clay and there was a threat these two could simply wear each other out.
Nadal did struggle during long rallies but broke his man in the first and third sets to claim the win 6-3 6-7 6-3.
Del Potro beats Haase in the 3rd round of Paris Masters.
Juan Martin Del Potro of Argentina serves the ball to Joao Sousa of Portugal and moved closer to securing the last spot for the season-ending ATP Finals by beating Robin Haase 7-5, 6-4 in the third round of the Paris Masters on Thursday.
Del Potro, who lost to Roger Federer on Sunday in the Swiss Indoors final, is in 10th place in the race to qualify for the tournament. Only the top eight players will compete in London and there is one place left, to be taken in Paris.
”I would love to reach London once again. It could be a fantastic moment for me,” said Del Potro, who was way back in 47th place in the race before the U.S. Open. ”I’m excited to keep improving for this kind of surprise. I love to surprise myself and that’s what I’m doing now.”
Del Potro has a tough challenge next, against big-serving American John Isner.
The ninth-seeded Isner, last year’s runner-up to Andy Murray, hit 25 aces as he beat sixth-seeded Grigor Dimitrov of Bulgaria 7-6 (10), 5-7, 7-6 (3).
Seventh-seeded David Goffin of Belgium was through to the finals in London, despite a surprise loss to unseeded Julien Benneteau 6-3, 6-3. The Frenchman reached the quarters of a Masters for the first time since Shanghai in 2014 in his final tournament before retiring.
Goffin will have waited nervously on the result of Frenchman Lucas Pouille’s result against Jack Sock. But Pouille’s 7-6 (6), 6-3 loss to the 16th-seeded American sent him through, at Pouille’s expense, making him the first Belgian to qualify for the season finale.
”I would have preferred to have qualified by winning and Lucas is a friend,” Goffin said. ”But I am still so happy to have qualified.”
Earlier, Dominic Thiem lost early again, this time falling to Fernando Verdasco 6-4, 6-4.
Since losing to Del Potro in five sets in the fourth round of the U.S. Open, the fifth-seeded Austrian has won only two matches in five tournaments.
Verdasco, meanwhile, next plays Sock in the last eight.
Also, Filip Krajinovic advanced with a 6-2, 3-6, 6-1 wins against Nicolas Mahut of France. The Serbian qualifier next plays Rafael Nadal or Pablo Cuevas.
Nadal, who is guaranteed to finish the year with the top ranking for the fourth time in his career, has never won the Paris Masters.