Schmiedlova, the world No. 83, was a set up when the match was stopped in Hiroshima, with Putintseva halting play in the opening game of the second set.
The Slovakian, who was knocked out of the US Open in the first round last month, looked comfortable in the first set and won 6-2 in 48 minutes.
"I'm really, really happy that I won today because I didn't win any matches in a few weeks," Schmiedlova told the WTA website. "She had some problem with her back, probably, so it wasn't as I wanted it to be. But I'm very happy that I can play the second round here."
Elsewhere, China's Saisai Zheng defeated American Alison Riske 7-5 6-4 to also advance to the second round. The 7th seed broke Riske's serve to win the second set and win the match in just over an hour.