Also through to the next round is Australian Open champion Stanislas Wawrinka, who looked sharp in a no-nonsense 7-5 6-4 win over Frenchman Edouard Roger-Vasselin. (Agencies)
Nadal, who has reached the final three times but never lifted the Miami title, blew past Lleyton Hewitt in the second round before overwhelming Istomin in less than an hour in a centre court master class.
Next up for the Spaniard is a fourth round meeting on Tuesday with Italian 14th seed Fabio Fognini, who advanced with a 4-6 6-3 6-3 comeback win over Spain's Roberto Bautista Agut.
Further down the road is a possible semi-final meeting with third seed Wawrinka, who beat the Spaniard in the final of the Australian Open to claim his first grand slam title.
Nadal has shown no signs of losing focus, however, and broke Istomin twice to open the match and grab a 4-0 lead.
The 57th ranked Istomin finally held serve at 4-1 but that would be the only time as Nadal thundered through the next eight game to complete the rout.
"I played a very complete match," said Nadal, who was given a warning for slow play. "No match is perfect but I did a lot of things very well. No mistakes, serving with good percentage, and playing a lot of winners.
"My movements were better than what I did last event events. That's a very important thing for me."
Wawrinka, who has admitted to suffering something of a grand slam hangover, has already matched his best effort in six visits to Miami. His win set up a last 16 meeting with Ukraine's Alexander Dolgopolov, a 3-6 6-0 7-6(5) winner over Serb Dusan Lajovic.
"Just doing my job. Simple," said Wawrinka. "My job is to play tennis, try to play the best possible, and to do that I have to practice well.
"People are expecting more from me but from myself it's the same. The pressure is same. I always put a lot of pressure on myself and always want to win matches and play well."
Canadian 12th seed Milos Raonic blasted his way into the fourth round with 6-1 6-2 win over Spain's Guillermo Garcia-Lopez in 56 minutes.
Raonic, who exited the Miami tournament in the third round with injuries the last two years, has had no fitness concerns this year, firing 10 aces and surrendering just five points on his serve to Garcia-Lopez.
Also through to the next round is Australian Open champion Stanislas Wawrinka, who looked sharp in a no-nonsense 7-5 6-4 win over Frenchman Edouard Roger-Vasselin.