Pegula, the world number five from the United States, had clawed back a set but was broken to trail 0-2 in the third before mounting a final fightback.
"All I just kept thinking was, like, welcome to the clay court season," Pegula said after grinding out the win on Charleston's green clay.
Pegula, who enjoyed a first-round bye, said the breezy conditions and challenging shadows made it hard to respond aggressively to the high, looping shots from 72nd-ranked Putintseva of Kazakhstan.
"She's a really tricky opponent in general," Pegula said.
"I feel like especially on clay she can be really crafty, use high balls, low balls, slices, drop shots, and I felt like she was just honestly toying with me there for quite a while," added the American, who was broken as she served for the match at 5-4 but broke back to give herself another opportunity to close it out.
Pegula is chasing her second title of the year, after a victory in Dubai in February.
Second-seeded Ekaterina Alexandrova withdrew from the tournament before her second-round opener on Wednesday, saying she had "a bit of an injury" picked up in Miami.
The 13th-ranked Russian was replaced in the draw by Ekaterine Gorgodze of Georgia.