Nadal was taken to four gruelling sets in almost four hours before winning 6-3, 6-7 (4/7), 6-3, 6-3 on Rod Laver Arena.
It will be his 10th Australian Open quarter-final appearance, second only to Roger Federer, and he will face Croatia's sixth seed Marin Cilic. Nadal leads 5-1 in their previous meetings.
It was the Spaniard's fourth win over the Argentine but his toughest after beating him in straight sets in the second round at the 2015 US Open.
"Of course, I feel little bit tired, but yeah good. I was able to keep fighting until the end," he said.
"It is the first big match I played in 2018. I started later than usual so a match like this probably helps because you know that helps confidence in myself.
"That's confidence knowing that I can resist almost four hours on court playing at a good intensity."
Nadal broke in the eighth game on the way to taking the opening set, but he encountered stiff resistance in the second set.
There was a magical moment when Schwartzman ran down a drop shot and won the point with an angled volley across the net to break back at 4-4.
Nadal took control in the third set with a break in the fourth game, but he had to fight off five break points before holding serve in a titanic 13-minute second game in the final set.
He broke in the third game of the fourth set, but had to make some monumental holds of service to keep Schwartzman at bay, winning on his third match point with a return winner.
He endeared the crowd with the scampering around the court and his astonishingly powerful groundstrokes for one so small in stature.
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