Nadal, who bizarrely hurt his knee while sitting in a chair the day before the tournament began, is one win away from a possible semifinal against old rival Roger Federer after beating his fellow Spaniard for the ninth time in 11 matches.
On a sunny day with the temperature rising to 32C (89F), both players sat with ice towels around their necks during the changeovers.
Nadal needed treatment from the trainer for a left ankle problem after three games of the first set. By that time, he had already broken serve and he did the same early in the next two sets to maintain control against his "very good friend" Lopez.
"I am fine," Nadal said. "It was a very, very hot day. I think it's positive to keep winning in straight sets."
Federer was up against 19-year-old Australian Bernard Tomic in the first match of the night session later Sunday. The 16-time Grand Slam champion hasn't been beaten by a teenager since 2006, when he lost to Andy Murray at the Cincinnati Masters.
Also Sunday, defending champion Kim Clijsters was to face Li Na in a repeat of the 2011 final. Clijsters beat Li 3-6, 6-3, 6-3 to win her fourth major title a year ago.
Victoria Azarenka was the first player to reach the quarterfinals when she beat Iveta Benesova 6-2, 6-2.
The third-seeded Belarusian is yet to drop a set at the tournament and will next meet eighth-seeded Agnieszka Radwanska, who beat Julia Goerges of Germany 6-1, 6-1.
With the win, 22-year-old Azarenka stayed in the hunt for the No. 1 ranking. Petra Kvitova and Maria Sharapova can also claim the top spot from Caroline Wozniacki.
"I would be a liar if I said I didn't care about it," Azarenka said. "It's in the back of my head and we'll take it day by day, I guess."
Azarenka, like Wozniacki, is aiming for her first Grand Slam title. She has never gone past the quarterfinals at the Australian Open, but goes into her match against Radwanska with a 6-3 winning record. The last of those victories came at the Sydney International tournament, which Azarenka won before coming to Melbourne.
Sunday's win was her ninth straight, but the likes of Serena Williams and Clijsters are still attracting more attention.
"For me, doesn't really matter. I try to focus on myself," Azarenka said. "I think I'm in the best shape physically right now, so it kind of helps other aspects of the game. I feel pretty good out there."