The world number one, playing his first tournament since losing the Australian Open final in January, admitted after his third round win over Albert Montanes that his sore back was still bothering him.
But his demolition job on Portugal's Sousa - a victory completed in just 75 minutes - suggests the ailment is not affecting the Spaniard too much once he steps onto the court.
The top seed now faces compatriot Pablo Andujar for a place in the final of the ATP500 claycourt tournament in Brazil.
Andujar booked his place in the last four with an equally impressive 6-1 6-1 drubbing of fourth seed and another Spaniard Tommy Robredo.
In the other half of the draw, David Ferrer ensured Spain would have three representatives in the semi-finals with a 4-6 6-3 6-3 victory over Brazilian Thomaz Bellucci, but not after a lengthy delay due to a floodlight failure.
The pair had to wait over an hour with Ferrer leading 2-1 in the final set before returning to the court after the lights went out on the outdoor stadium.
"It was really tough," Ferrer said. "When the match was stopped it was practically in my hands. It was bad luck with what happened with the lights."
After posting the victory, Dolgopolov confirmed he would stay and play out the tournament rather than returning to his homeland, which is currently engulfed by protests and violence.
"I don't think it's going to change a lot at this point if I just finished playing and come back to my country," said Dolgopolov. "It's still going to be the same situation. I will just be closer. But I am not considering that at this moment."
At the Delray Beach Open American qualifier Steve Johnson won through to his first ATP Tour semi-final after an emphatic victory.
The 24-year-old, who eliminated top seed Tommy Haas in the second round, dominated sixth seeded Spaniard Feliciano Lopez to win their quarter-final 6-3 6-2 in 73 minutes.
Johnson did not drop serve and broke Lopez three times.
"I stuck to the game plan and executed really well and in the end I was able to hold my nerves," he said.
Johnson, ranked 142nd in the world, will meet 2012 champion Kevin Anderson in the semi-finals on Saturday.
Johnson might be the underdog against fourth seed Anderson, but will take confidence in the knowledge he beat the South African in Auckland in January.
Anderson advanced to the semi-finals with a 6-7(3) 6-3 6-3 victory over Australian Marinko Matosevic.
"I just hung in there and finally got that breakthrough in the second set," said Anderson, who dropped serve once in the gusty conditions.
The other semi-final will pit Croatian Marin Cilic against American John Isner.
Seventh-seed Cilic advanced with a comfortable 6-3 6-2 win over Russian Teymuraz Gabashvili.
"Good times are rolling," Cilic said after serving 12 aces.
He also returned well, breaking Gabashvili five times.
It was Cilic's 11th straight-set victory in 13 matches since a second round exit at the Australian Open as he stayed on track for his third final in as many weeks.
He lost the final in Rotterdam last week, and won the week before on home soil in Zagreb.
Second seed Isner dropped the first set against Rhyne Williams, but recovered to beat his American compatriot 4-6 6-3 6-2.
The big-serving Isner pounded down 18 aces and only lost five of 45 points on his first serve.
Rio de Janeiro Open results
1-Rafa Nadal (Spain) beat Joao Sousa (Portugal) 6-1 6-0
8-Pablo Andujar (Spain) beat 4-Tommy Robredo (Spain) 6-1 6-1
2-David Ferrer (Spain) beat Thomaz Bellucci (Brazil) 4-6 6-3 6-3
Alexandr Dolgopolov (Ukraine) beat 3-Fabio Fognini (Italy) 6-1 6-1
Delray Beach International results
2-John Isner (U.S.) beat Rhyne Williams (U.S.) 4-6 6-3 6-2
7-Marin Cilic (Croatia) beat Teymuraz Gabashvili (Russia) 6-2 6-3
Steve Johnson (U.S.) beat 6-Feliciano Lopez (Spain) 6-3 6-2
4-Kevin Anderson (South Africa) beat Marinko Matosevic (Australia) 6-7(3) 6-3 6-3
- Sports & Recreation
- Pablo Andujar
- Alexandr Dolgopolov
- David Ferrer
- Thomaz Bellucci