The former world No 1, who is battling back from hip surgery, saw off the Uruguayan 6-4 6-3 in just under 84 minutes in Belgium and revealed afterwards that he is feeling sharper with each match he plays – even if it is taking him longer to get up to full speed.
World No 45 Cuevas saved seven break points in the first set but was eventually undone in the tenth game, allowing Murray to take the opener.
Murray, who is now ranked 243, broke again in game six of the second set to lead 4-2 and there was then no way back for Cuevas as the Scot finished the job.
Murray will now play Romania’s Marius Copil, the world No 92, in the last eight.
The former world No 1 has won his first matches at ATP Tour level in 16 months in this tournament but the event is likely to be his last of the year, with the possible exception of the Davis Cup next month.
With his third child due, he is planning a month-long break and he could even leave Antwerp early if his wife Kim goes into labour.
“I’m enjoying the tournament so far, I’m enjoying the city and hope I can stay here for a few more days,” said Murray, who has surprised many with the level at which he has been able to play only eight and a half months after hip resurfacing surgery.
“I think it’s getting there,” he said of his sharpness. “It sometimes takes me a little bit longer to get going, but it was a good day.”
Greg Rusedski believes the Scot still has a long road ahead if he is to return to the very top of the game.
In a three-week stint in China, Murray beat now world No 11 Matteo Berrettini and pushed Dominic Thiem and Fabio Fognini hard in close defeats. It was a big step up from the performances Murray produced on his return to singles action in America in August and raised the prospect that he could perhaps again challenge for the game’s biggest titles.
But, after two years of struggles with his right hip and at the age of 32, Rusedski believes it is too early to make future predictions for Murray.
The former British No 1 said: “I’ve been pleasantly surprised. I thought it would be much more difficult for him, I thought it would take a little bit longer, but he’s played very, very well.
“The question mark is still how much can his body take week in, week out. There’s still a long road back.
“He’s played two matches back to back, but can he play three, four, five days in a row? It’s too hard to predict. I think we’ll know more when he plays the Australian Open and a three-out-of-five-set match.
“It’s not his mentality or his tennis, it’s what the body will allow him to do. But the signs are very positive.”