Sonmez, who continued her solid form to end last year, has enjoyed huge support from Turkish fans at Melbourne Park this week.
Faults and unforced errors from Putintseva were routinely cheered by the raucous crowd in Kia Arena.
The Russian-born Putintseva was stunned by what she experienced in the 6-3 6-7 (7-3) 6-3 third-round win on Friday.
"There is always someone in favour and someone to cheer for, that's what's great about the sport," the world No.94 said.
"But today I think was really a lot of disrespectful moments when they were screaming between my first and second serve.
"Screaming ... really loud to make me mistake.
"It 4-3, was a big point, opened court very good, I take my forehand, the guy just started coughing just for my shot.
"I was like, OK now, I'm not going to lose.
"I was ready to take it all, but I was ready to fight like until I die there.
"It's just some people have education of tennis and, some of them not.
"They were disrespectful in the moment when it was important, and they could see it's important."
Putintseva will face 29th seed Iva Jovic in the fourth round after the American teen sensation knocked out Italy's world No.8 Jasmie Paolini.
It is her best result at Melbourne Park in her 14th appearance at the first grand slam of the year.
Putintseva has previously reached quarter-finals at Roland Garros the US Open.
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