Fognini occupied Nadal for 63 minutes, nine minutes longer than Nadal's second-round match.
"Of course, it's good news, and especially in this part of the season," Nadal said. "It's better like this than having long matches. You save a little bit more the body.
"It doesn't matter how long you are on court, [the] most important thing is be enough competitive to [handle] all the situations."
Nadal hadn't won an ATP hard-court title in more than three years until the US Open last month, and now he's gunning for his third in five weeks.
Nadal saved both break points he faced in the round-of-16 match, in the fourth game of the second set.
Federer will play Richard Gasquet in the quarterfinals.
Del Potro required four match points -- two on Zverev's serve in the ninth game, two on his own serve in the 10th game -- to win his first encounter against the German.
Del Potro, who lost his serve for the only time in the match in the second game, won nine of his 15 service games at love.
Zverev, in the hunt for a sixth ATP title of the season, lost his composure after netting a backhand to surrender his serve in the fifth game of the third set to the Argentine. He repeatedly smashed his racket until it was a mangled mess.
"For me, it's impossible to lose a match when I've only been broken one time," Zverev said. "The game where he broke me, I was up 40-15, and I was just unfocused there."
Del Potro knew Zverev's reaction to losing serve was likely a good omen.
"I saw his frustration, for sure," del Potro said. "He's still very young and has to keep learning. He has everything to be in the top of the game."
Del Potro will meet Viktor Troicki of Serbia in the last eight on Friday.