Nadal and sixth-seeded American Andy Roddick both advanced without having to hit a ball after their respective opponents -Germany's Philipp Kohlschreiber and 10th-seeded Russian Nikolay Davydenko - withdrew with leg injuries.
Second-seeded Roger Federer also made it to the quarters by beating 14th-seeded James Blake of the United States 6-2, 6-4.
The last time the two met, in China, Blake ended Federer's hopes of capturing his first Olympic singles medal.
"We haven't played since the Olympics and I was pleased with the way it went today, especially with him playing so well recently,'' Federer said.
Federer will next play Roddick.
"I've played Andy so many times it's time we played each other on clay,'' Federer said of his next opponent.
Murray had failed to convert seven break points before finally getting the decisive breakthrough to go up 6-5 and then held serve to take the first set.
"I was a little tense when I had my chances and didn't take them,'' Murray said.
Murray, who turns 22 on Friday, then began hitting long, accurate baseline shots and well-timed passers to dominate the second.
"I noticed that at this altitude the ball tends to fly faster, and because the court is sprayed with water regularly the balls also tend to pick up weight,'' Murray said. "I strung my rackets more tightly to compensate and was happy to be able to control the ball in the wind here.''
The 16th-seeded Robredo said he simply couldn't recover after giving up an early break in the second set.
"If you don't take your chances when you've got them, then he's going to kill you,'' Robredo said. "When you attack him he defends well, and if you let him attack he really does it.''
Third-seeded Novak Djokovic won against Andreas Seppi of Italy 6-4, 6-4.
In the third round of the women's event, No. 1 player Dinara Safina of Russia played aggressively to win the first set against Lucie Safarova of the Czech Repubic to love.
But Safina's concentration level then dropped and she lost the second 4-6 before sealing the match 6-3 in the third.
"Suddenly I started to play passively, even fearing the way the wind changed,'' Safina said. "Thankfully Safarova made some mistakes which let me win.''
Meanwhile, Agnes Szavay of Hungary rallied to beat seventh-seeded Victoria Azarenka 4-6, 6-2, 6-2, while earlier, Alona Bondarenko of Ukraine defeated Anna Chakvetadze of Russia, 6-0, 2-6, 6-3.
