The unseeded Indian dispatched the Frenchman 6-3 7-5 in one hour and 11 minutes.
Myneni saved all eight break points he faced and broke his rival twice on the match. Olivetti also struggled with unforced errors as he committed eight double faults to three of Myneni.
Myneni comfortably closed the contest in which he won 72 points to 54 of his rival.
Myneni needs to more wins to make it to the singles main draw of the last Grand Slam of the season and he next faces American Mitchell Krueger, who knocked Serbia's Nikola Milojevic 6-1 3-6 6-3.
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