The 25-year-old Nadal pulled out a 7-6 (7/5), 6-7 (4/7), 7-6 (11/9) victory over Verdasco in three hours and 37 minutes to reach the quarter-finals of the ATP and WTA hardcourt tournament.
"The truth is that I am very happy," Nadal said between singles and doubles matches. "Very content with the victory. It was a tough match for both of us."
The second-seeded Nadal improved to 12-0 lifetime against the unseeded Verdasco, who committed 41 unforced errors to 31 for Nadal.
"You enjoy always a good match," Verdasco said. "But when you lose in this way, of course it's not easy to lose. You have it so close. Tennis is like that."
Nadal hit fewer winners than Verdasco -- 29 versus 48 -- but was more consistent with his mixture of shots and had just two double faults compared to seven for his opponent.
For the second consecutive match, Nadal played with two fingers on his right hand bandaged after he burned them while grabbing a hot plate at a restaurant earlier this week.
Nadal next faces American seventh seed Mardy Fish, who outlasted France's Richard Gasquet, 7-5, 7-5.
Fish has lost all six career matches against Nadal dating back to 2006.
"I've never beaten him before," said Fish. "We'll come up with a game plan. Just off the top of my head I will be aggressive. I'm not a counterpuncher.
"If you're not going to get up for playing Rafa Nadal in the quarters of a huge tournament like this, then you've got issues."
In other men's third round matches on Thursday, Czech Tomas Berdych beat Nicolas Almagro of Spain, 6-2, 6-2, and fourth-seeded Briton Andy Murray defeated American Alex Bogomolov, 6-2, 7-5.
On the women's side of the draw, fourth seed Maria Sharapova cruised past Russian compatriot Svetlana Kuznetsova, 6-2, 6-3, Aussie Samantha Stosur upset Li Na of China, 6-4, 3-6, 6-4, and second seed Vera Zvonareva routed qualifier Petra Martic, 6-2, 6-2.
Serena Williams pulled out of the event Wednesday with a toe injury, which allowed Stosur to receive an extra day of rest before facing Li, the reigning French Open champion.
"I wasn't complaining that she pulled out," said Stosur. "I had a pretty easy day, which was nice, considering the week I had before. So I guess that was good for today's match, and hopefully will be good for tomorrow."
Stosur has beaten Li three times this season.
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