Saketh, ranked 143rd in the ATP chart, now has a chance to play in the singles main draw of a Grand Slam for the first time in his career as he faces Pedja Krstin from Serbia in the third round.
The big-serving Indian had lost in the third Qualifying round at the Australian Open and bowed out in the second round of the French Open early this year.
In the second set, it was Myneni, who drew first blood in the seventh game and served out the match in the 10th after battling hard for one hour and 30 minutes.
The Indian now needs to down his Serbian opponent, who is placed 57 places below him at 200 in the ATP rankings.
However, Pedja goes into the contest 1-0 up in Head-to-Head record with a win over the Indian in Turkey in May last year.