After racing through the first set, Kudryavtseva was suddenly forced into the role of spectator in her return games as Tomljanovic's powerful delivery turned the tables. As she grew in confidence, Tomljanovic's own returning began to look increasingly threatening, and a break midway through the second leveled the match at one set all.
The pattern continued in the decider and with each quick-fire service game from the Croat, the pressure built down the other end.
"Serving was very important in the third set as she was hitting really big serves and I was struggling to stay in those games and wasn't getting many points," Kudryavtseva said.
The breakthrough came in the 11th game, presenting Tomljanovic with the chance to serve for the match. She could not take it, though, as the Russian rediscovered her return game in the nick of time, reeling off 11 of the next 14 points to close out an improbable 61 36 76(2) victory.
"I started to get into her games a bit more at the end of the set and that was a big deal for me and gave me a lot of confidence for the tie-break," Kudryavtseva added. "I think she started to feel the pressure as my returns got better, which played on her mind a bit."
Meeting Kudryavtseva in the second round will be Alison Van Uytvanck, after she defeated Olga Puchkova, 61 63. Also advancing were Dinah Pfizenmaier, who fought back to see off Stéphanie Dubois, 67(7) 63 64, and Daria Gavrilova, who edged past fellow Russian Vera Dushevina, 76(2) 76(3).