The former world number one, who is battling back from hip surgery, saw off the Uruguayan 6-4 6-3 in just under 84 minutes in Belgium.
World number 45 Cuevas saved seven break points in the first set but was eventually undone in the 10th 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 number 92, in the last eight.
Murray 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.