Victories over Ryan Harrison, Casper Ruud and Alexandr Dolgopolov set up a mouth-watering contest against Spaniard Nadal.
Nadal, 31, won the opening set 6-3 before Schwartzman, seeded 24 in Melbourne, hit back superbly to level the match after winning a second set tie-break 7-4.
But it was Nadal who managed to overcome the gutsy Argentinian Davis Cup star 6-3 6-3 on Rod Laver Arena to set up a last-eight meeting with Croatia's Marin Cilic.
"It was a great battle. He is a good friend of mine," said Nadal
"He is a great player, in all aspects, and I feel that for a lot of moments he was serving well.
"I was able to keep fighting until the end and it is the first big match I have played in 2018.
"It probably helps my confidence, knowing I can resist almost four hours on court."