To make it to the main draw, Saketh needed to win three rounds in the qualifiers and he made it with minimum fuss without dropping a single set.
In the earlier rounds, Myneni, seeded 26th, won 7-6 (6) 6-4 over local lad Mitchell Krueger. Myneni beat Albano Olivetti of France 7-5 6-3 in the first round.
The last two Indians to have qualified for a singles Grand Slam tournament proper were Yuki Bhambri and Somdev Devvarman.
Pedja went into the contest 1-0 up in Head-to-Head record with a win over the Indian in Turkey in May last year but proved to be no match for Myneni on the day.
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In the first set, Myneni broke Pedja thrice while the Serbian broke him once with the duration being 30 minutes.
The second set finished in only 26 minutes as Myneni broke him thrice and wrapped up the match in style.
Myneni said he was very happy to cross the qualifying hurdle.
"Playing in a home away from home Grand Slam was something big and very motivating. I have been pushing and came short on a few occasions before but very happy that I got over the first step this time around.
"The process of learning to get better and perform at the big stages is always something that I look at. I wanted to use my experiences from some of the close encounters I had in the recent times and try to play smart tennis," he said.
"I got couple days to recover and try to prepare myself for the main draw, which starts on Monday. Hopefully, I will bring the best tennis out and try to perform at the big stage," said Myneni.