The 31-year-old Verdasco, who is ranked 34th in the world, has now won his last two matches against world number three Nadal, after the 14-time grand slam winner had won their previous 13 meetings.
"It is a huge victory and it is always nice to win in a packed stadium in a big tournament and against one of the best players in history," said Verdasco.
Verdasco caused problems from the outset and broke in the eighth game, helped by a double fault from Nadal.
Nadal battled back in the second set, breaking Verdasco twice and pushing the contest into a third set.
The contest turned decisively in Verdasco's direction when he broke to go 3-1 up in the third set.
Nadal has never won in Miami, with his 11 attempts his longest streak of attempts at a tournament without a victory and he said he was concerned that he was nervous when playing.
"I am playing with too much nerves for a lot of moments, in important moments, playing a little bit of anxious in those moments," he said.
"I have been able to control my emotions during, let's say, 90-95 percent of the matches in my career, today it was tougher to be under self control.
"But I am going to fix it. I don't know if in one week, in six months, or in one year, but I am going to do it."
In another upset, seventh seed Stan Wawrinka lost 7-6(4) 7-6(5) to 28th-seed Adrian Mannarino.
Britain's Andy Murray moved into the last 16 after beating Colombia's Santiago Giraldo 6-3 6-4 to clinch his 499th win on the ATP Tour.
Murray would become just the ninth active player and only the 46th man in the Open era to achieve the 500-win milestone should he defeat South African Kevin Anderson in the next round at Key Biscayne.
Murray's latest win, in bright sunshine, was a relatively straightforward matter although Giraldo's free swinging approach in the second set brought the contest alive as he battled back from 5-1 down before Murray wrapped up the win in 84 minutes.
Czech Tomas Berdych saved four match points as he beat Australia's Bernard Tomic 6-7(4) 7-6(3) 6-1.
(Editing by Gene Cherry/Greg Stutchbury)
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