Officials announced a suspicious package had been left near the main entrance to the sprawling tennis facility which was quickly locked down, keeping thousands of spectators from entering or leaving while Miami Dade police investigated.
The all clear was given just before Nadal stepped onto the Crandon Park centre court to face Fognini in the final match of the night.
The Spaniard showed no signs of being alarmed by the bomb scare as he completed the win in 62 minutes.
"Every day I have to try to find my rhythm, try to think about myself, what I have to do well, so I just try to be focused on what I really need to do to play well," said Nadal.
"Then the opponent is free to do whatever. Tonight was not an easy match for him, for the conditions that I told you before. So it was a little bit strange, but in general, I think I was very focused and solid with my serve."
"He's a very dangerous opponent," added the Spaniard.
"His serve is huge, one of the best without any doubt, and he's able to play very aggressive on the return because he doesn't feel a lot of pressure on his return because he knows that he's very safe with his serve."
Nadal's great rival Federer was also in cruise control, needing just 49 minutes to dismiss ninth seeded Frenchman Richard Gasquet 6-1 6-2.
"Look, things went well out on the court today," said the Swiss 17-times Grand Slam winner. "You just take what you get and you run with it.
"I think I played well. I served well. I made my returns I had to and stayed aggressive, so I didn't let him just make errors.
"I forced him to do stuff. It was a good match for me."
Defending champion Murray, playing his first event since splitting with coach Ivan Lendl last week, has looked increasingly comfortable and confident on his own.
He disposed of 11th-seeded Frenchman Jo-Wilfried Tsonga 6-4 6-1 without facing a single break point.
Djokovic, a three-times winner on the Miami hardcourts, had only two break points the entire match but that was all the second seeded Serb needed, converting both chances on his way to a 6-3 7-5 win over Spaniard Tommy Robredo.
Dolgopolov battled to a 6-4 3-6 6-1 win over Swiss third seed and Australian Open champion Stanislas Wawrinka, while Nishikori shocked fourth seeded Spaniard David Ferrer 7-6(7) 2-6 7-6(9).
In other fourth-round action, big-hitting American John Isner was beaten 6-3 7-5 by Czech seventh seed Tomas Berdych.
While the day got off to a gloomy start with early morning showers delaying play by 30 minutes, tennis fans were treated to a line-up of sparkling action with nine of the world's top 10 men battling for spots in the quarters.
Djokovic, riding the momentum from his Masters Series win in Indian Wells nine days ago, was first through to the last eight and was soon followed by Murray, setting up rematch of last year's Wimbledon final won by the Briton.
It was just the second match of the tournament for Djokovic, who received an opening-round bye and advanced to the last 16 on a walkover when Florian Mayer withdrew with a groin injury.
"Very solid win," said Djokovic. "I just was telling myself to stay mentally tough out there and composed and not get carried away by few points.
"I have done well. I have served well. I made him play an extra shot in important moments and that's why I'm satisfied with the overall match today."
Murray, fighting for form after undergoing off-season back surgery and going solo after ending his successful partnership with Lendl, finally seemed to put some of the distractions behind him, although he requested pain relief tablets for his back during the first set.
"We played each other a lot obviously," said Murray looking ahead to Wednesday's quarter-final. "We have played each other here three times, I don't know, maybe four times.
"You know, the conditions can change a lot here. Obviously it can be extremely windy or very hot and humid.
"Ultimately whoever deals with those things better on the day and whoever plays better will win.
"Whether I beat him the last time or he beat me the last three or four times, I don't think it matters too much."
Miami Masters results
1-Rafa Nadal (Spain) beat 14-Fabio Fognini (Italy) 6-2 6-2
7-Tomas Berdych (Czech Republic) beat 10-John Isner (U.S.) 6-3 7-5
12-Milos Raonic (Canada) beat Benjamin Becker (Germany) 6-3 6-4
5-Roger Federer (Switzerland) beat 9-Richard Gasquet (France) 6-1 6-2
22-Alexandr Dolgopolov (Ukraine) beat 3-Stanislas Wawrinka (Switzerland) 6-4 3-6 6-1
6-Andy Murray (Britain) beat 11-Jo-Wilfried Tsonga (France) 6-4 6-1
20-Kei Nishikori (Japan) beat 4-David Ferrer (Spain) 7-6(7) 2-6 7-6(9)
2-Novak Djokovic (Serbia) beat 16-Tommy Robredo (Spain) 6-3 7-5
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