Nadal eased past Frenchman Benoit Paire 6-3, 6-4 and will next face either compatriot Nicolas Almagro or Mikhail Youzhny of Russia for a place in the quarter-finals.
One break in each set was enough for Nadal as he overcame some impressive variety and touch shown by Paire early on to break when the world number 37 was serving at 2-3 down in the opening set, before eventually sealing it 6-3.
Paire had his only look at a break point on the Nadal serve early in the second set but couldn't take advantage, and in typical Nadal fashion he upped the pressure to break at 4-4 before serving out to book his place in the last 16.
Nadal insisted that it would be "arrogant" to consider himself the title favourite following the shock exit of world number one Novak Djokovic at the hands of Grigor Dmitrov on Tuesday.
"I'm not looking beyond the next round, it would be arrogant to do that so I am not going to do it," said Nadal.
The seven-time French Open champion has compiled a 27-2 match record this year after missing seven months of with a knee injury.
That run has included trophies in Sao Paulo, Acapulco, Indian Wells and Barcelona.
Spanish fourth seed David Ferrer also made the last 16 with a 7-5, 6-2 win over Denis Istomin of Uzbekistan.
Last year's finalist and sixth seed Tomas Berdych stayed on course for a quarter-final meeting with Andy Murray as he recovered from a set down against Jerzy Janowicz to win 6-7 (3/7), 6-3, 6-2.
German 13th seed Tommy Haas, the champion in Munich last weekend, saw off Tommy Robredo 6-3, 7-5 while French seventh seed Jo-Wilfried Tsonga beat Dutchman Robin Haase 7-6 (7/5), 7-6 (7/1).
Japanese 14th seed Kei Nishikori will face Roger Federer in the third round after he beat Victor Troicki 7-5, 6-2.
On the women's side there was a big upset as world number three Azarenka crashed out to Russian Ekaterina Makarova 1-6, 6-2, 6-3.
Azarenka had looked as if she would cruise into the last 16 early on as she dominated the world number 24 in the first set.
However, Makarova turned the match on its head in the second set as she broke early on and again with Azarenka serving at 2-5 to force the match into a decider.
There were even more twists and turns in the third as Azarenka again appeared to take control as she surged into a 2-0 lead, but the double Australian Open champion then fell to pieces with a string of unforced errors that allowed Makarova back onto level terms at 3-3.
Azarenka was then unhappy when she was docked a point by the umpire for smashing her racket in the next game as Makarova moved ahead for the first time in the set.
Azarenka, who had a 17-0 winning record on court this year going into the tournament, blamed her exit on a lack of match practice due to an injury that had kept her out for two months.
"I think it was really noticeable. I made mistakes that I don't normally do, but that's what comes after not playing for a long time," she said.
"I still have another tournament before the French Open to compete in, and I'm going to go back on the practice court as I always do and work hard to improve."
German sixth seed Angelique Kerber was the first woman into the quarter-finals with a 3-6, 6-4, 7-5 win over former French Open and US Open champion Svetlana Kuznetsova.
Serb 14th seed Ana Ivanovic also made the last eight, coming from 2-5 downin the final set to beat Britain's Laura Robson 5-7, 6-2, 7-6 (7/5).