World No. 2 Nadal took an hour and 45 minutes to reach the quarterfinals at the All England Club for the seventh time in his career as a pro.
Following the traditional Sunday rest day, Nadal returned to the central court to show off how speedy his legs were and how effective his service was, which he held successfully, not allowing Sousa to create a single break point in the whole match, Efe news reported.
The 33-year-old Spanish star thus extended his head-to-head record against Sousa to 3-0, in which Nadal lost just one set in the 2016 Madrid Masters quarterfinals.
"It was a solid match...The second serve didn't work as well as two days ago (against Jo-Wilfried Tsonga), but the rest was very positive," third seed Nadal said after the match.
"I'm happy to be where I am, the body is holding well and I'm playing some good tennis," he added.
It became Nadal's 70th overall win on grass, and the 36th this season on all surfaces.
Swiss tennis icon Roger Federer is expected to equal the Spaniard's record this season if he defeats Matteo Berrettini of Italy later in the day.
In the quarterfinal, Nadal is pending the winner of the all-American duel pitting Sam Querrey against Tennys Sandgren.
The Spaniard has a 4-1 head-to-head victory record against Querrey, but it would be their first meeting on grass. Nadal has never played Sandgren before.
Querrey's only win over Nadal came when he stunned the Spaniard in the final of the 2017 Mexico Open.
Spain's Roberto Bautista Agut made it to the quarterfinals with a 6-3, 7-5, 6-2 win over Frenchman Benoit Paire. Next up, Bautista will face either Guido Pella of Argentina or Canada's Milos Raonic.
( With inputs from IANS )