Having gone two sets up with big hitting from the baseline, towering sixth seed Anderson threw Schwartzman a lifeline while serving for the match at 5-4 and his booming serve faltered again at 5-6 as the Argeentine took the third set.
The 25-year-old Schwartzman, who won the Rio Open claycourt title earlier this year, switched gears in the tiebreak at the end of a tight fourth set to level the contest at two sets apiece as a tiring Anderson failed to earn a point.
With momentum having swung his way, Schwartzman secured the decisive breaks in the final set and sealed a memorable victory over the U.S. Open finalist with an ace after a contest lasting three hours and 51 minutes.
"He was very aggressive. One way or the other he started lining up points and it was different from what I had imagined, because he's more of an aggressive player," Schwartzman said.
"In the third set I tried on a crossover backhand to play better. And from then on he started getting a bit tired and he wasn't as accurate, unlike in the first two sets.
"I tried to take advantage of an opportunity. I was lucky, because I took advantage of two of his mistakes when he was serving for the match."
Schwartzman, who became only the eighth Argentine to reach multiple Grand Slam quarter-finals in the Open Era, next faces top seed Rafa Nadal who beat Maximilian Marterer. He trails Nadal 5-0 in their previous meetings.
"Always I believe I can do (it). If not, I'm not playing tennis," Schwartzman added. "But Rafa here, I know it's his second home, and it's going to be a really tough match.
"I need to recover well, because against him I need to run a lot and do my best. I need to be ready for the next match and do my best," he added.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Matthew Mpoke Bigg and Ken Ferris)
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