Entered as a qualifier as she continues her comeback after an ACL injury, Saville looked headed for a second-round exit against the German world No.47.
With the score 5-7 4-5 and trailing 30-40, a sweeping forehand dropped into the back corner to save the match before the Australian pulled off a remarkable 5-7 7-6 (7-2) 6-2 victory.
"It was a fun match only because I won in the end," said a laughing Saville after a clash that lasted three hours and 14 minutes.
"It was a tough battle."
It was Saville's fourth top-50 win of the season, with the 29-year-old former world No.20 projected to return to the top 120, up from 148.
Saville will next face the winner of world No.26 Emma Navarro, the tournament's third seed, and Czech Katerina Siniakova.
In other second round results, Perth teenager Taylah Preston fell to Ukrainian world No.34 Marta Kostyuk 6-4 6-3.
Preston enjoyed her first tour-level main draw success in the first round, downing Magdalena Frech.
Last week, she reached the biggest singles final of her career at the WTA 125 tournament which moved her to a career-high ranking of 153.
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