Kozlov was Spaniard’s practice partner on Monday when he was called in as a last-minute replacement for injured Frenchman Maxime Cressy in the main draw.
Barring a brief period in the second set when he converted his only breakpoint chance in the contest, Kozlov was no match for Nadal whose previous best start of 11-0 in 2014 ended with a defeat to Swiss Stan Wawrinka in the Australian Open final.
Next up for the 35-year-old will be another American in 39th-ranked Tommy Paul with a potential semifinal clash against top-seeded Russian Daniil Medvedev, who he defeated in the Australian Open final from a two-set deficit.
“It’s always important to win as quickly as possible, but the most important thing is to win,” Nadal said after his victory in an hour and 16 minutes in hot and humid conditions.
“Tonight has been straight sets, that’s great news, and I’ll try to be ready for tomorrow again against a tough opponent.”
Medvedev earlier crushed Pablo Andújar 6-1 6-2 and put himself three wins away from victory at the tournament and rising to the world number one ranking for the first time.
Medvedev pretended like he might serve underhand on match point but instead thumped his seventh ace, eliciting a smile from the 68th-ranked Spaniard who played well but who could not break down the Russian’s firm defense.
Medvedev will next face Japanese qualifier Yoshihito Nishioka and a title on Sunday for the Russian will guarantee his ascent to the world number one ranking replacing Serbian Novak Djokovic.
World number four Stefanos Tsitsipas also wasted little time in dispatching American qualifier JJ Wolf, the French Open finalist sprinting to a 6-1 6-0 win in just 47 minutes in the last match of the evening on the main showcourt.
It was the 23-year-old Greek’s fastest completed win in his career and he will next meet 59th-ranked American Marcos Giron, who previously defeated Spaniard Pablo Carreño Busta 6-7 (7) 6-4 7-6 (4), for a place in the semifinals.