Kudermetova had a heavily-strapped right shoulder and required eye drops on changeovers, but still managed to sneak across the line for her first win at a Grand Slam.
The 22-year-old becomes the second Russian to cause a big shock in the opening week after compatriot Anastasia Potapova beat Angelique Kerber on Sunday.
"I think I played really well in the first set. I played aggressive. I played the way I wanted to play. And then I think she got very lucky in the start of the second set and... took advantage of the opportunities she got," Wozniacki told reporters.
"And then I just lost a little steam in the end and I made some unforced errors that I normally don't do, so that was very frustrating."