Kvitova out-served Rybakina 6-3, 7-5 who has already crashed out early in her last two tournaments going into the Australian Open.
This is the second time that the two players have gone up against each other. They first met in Ostrava last year. Their Head to Head record is now at 1-1.
Kvitova is a two-time Wimbledon champion. She won in 2011 and again in 2014.
“I tried to play faster than Elena. She played really great [in Ostrava]”, said Kvitova.
“It was a good match and I know that she’s serving really well,” Kvitova said on the court. “I was focusing on my serve and I was trying to wait for some chances to break her.”
“My serve really worked well today, so that’s what I’m really happy [with].”
“We didn’t really have a lot of rallies, so it was about the serve and the first one, two points of the rally. I’m glad that I was there for every shot.”
Rybakina missed her first serve and Kvitova took full advantage, losing only 14 points in 11 service games overall.
Kvitova will next go up against Zheng Qinwen in the second round. Zheng beat American Shelby Rogers in the first round.
Other players who advanced into the second round include Beatriz Haddad Maia, Amanda Anisimova, Barbora Krejcikova, and Daria Kasatkina.