As police closed the lone public entrance and exit to the grounds and shut down most traffic on the main highway of Key Biscayne island on the basis of an unattended backpack, Nadal took to the court and demolished out-of-sorts Italian 14th seed Fabio Fognini 6-2, 6-2 in 62 minutes.
Fognini played while injured as he lost to the Spaniard for the fourth time.
"Today was a very strange match. I'm sorry for Fabio," said Nadal. "He felt something from yesterday near the ribs. It was not easy for him to play this match.
"I managed the situation well in the wind. I played the right match."
Nadal will next play Canadian 12th seed Milos Raonic, who beat Benjamin Becker 6-3, 6-4 to win his 100th career hardcourt match.
Defending champion Andy Murray and Novak Djokovic will meet for the first time since last year's Wimbledon final after advancing with ease.
Wimbledon winner Murray dispatched French 11th seed Jo-Wilfried Tsonga 6-4, 6-1 while second seed Djokovic gave away a second-set point in a sporting gesture to Tommy Robredo during a 6-3, 7-5 triumph.
Britain's sixth-seeded Murray, who trails Djokovic 8-11 in their all-time rivalry, was looking forward to a repeat match with the Serb after not playing him since last July.
"We've played a lot and we always have long, tough matches. This will be a good test for me," Murray said.
Swiss fifth seed Roger Federer ousted French ninth seed Richard Gasquet 6-1, 6-2 in 49 minutes to book a quarter-final date with Japan's Kei Nishikori.
Federer was on fire against Gasquet, who set up two Federer match points with a backhand error and took the loss moments later as he could not reach a drop shot in the windy conditions.
"The wind was the same for both of us, but I've had a lot of experience playing in it," Federer said. "I made him work for his points.
"It was a great match for me and I'm very pleased," said Federer, who broke five times and committed only eight unforced errors.
Federer, who lost to Djokovic earlier this month in the Indian Wells final, won the Miami title in 2005 and 2006. His 79 career crowns include a record 17 Grand Slam titles.
Sore Murray moving well
Murray, who underwent back surgery six months ago, improved to 9-1 against Tsonga, advancing in 74 minutes.
The Scotsman, who converted on eight of his 12 break chances, won on his second match point as the Frenchman hit the net with a return.
"It was a close match," Murray said. "I had lots of break points. Conditions were tricky with the wind. It was not pretty tennis but we tried the best we could."
Despite reporting some pain in his hips and lower back, Murray was satisfied with his level of fitness while remaining aware that he needs to monitor himself.
"I haven't seen my physio. I chatted to him a little bit after the match, but I need to get assessed and have him treat me. Hopefully I'll be OK," Murray said.
"It was a bit sore but I still moved well throughout the rest of the match, which is a good sign. I was probably moving better at the end of the match than I was at the beginning, so that's probably a good sign."
Nishikori saved four match points in upsetting Spanish fourth seed David Ferrer 7-6 (9/7), 2-6, 7-6 (11/9).
Also advancing with a shock win was Ukraine's Alexandr Dolgopolov, who ousted Australian Open champion Stanislas Wawrinka, the Swiss third seed, by 6-4, 3-6, 6-1.
Dolgopolov, 7-3 against top-20 players this year, will meet Czech seventh seed Tomas Berdych, who beat US 10th seed John Isner 6-3, 7-5.