SYDNEY, Jan 10 (Reuters) - Two-times Wimbledon champion Petra Kvitova survived a scare against Arantxa Rus in her opening match of the Sydney Tennis Classic on Monday, coming back from a set down to win 3-6 7-6(4) 7-5 and reach the second round of the WTA 500 tournament. Czech Kvitova was stunned by Priscilla Hon in the first round at Adelaide last week and came close to another shock as she lost the opening set tamely against the world number 66 and was then dragged into a second set tiebreak. However, Kvitova clawed her way back to level the contest at one set each and saved two match points in the decider before wrapping up the near three-hour match on Ken Rosewall Arena. "I really had to fight a lot. I lost my first match in Adelaide and after losing in the beginning of the season, you don"t feel the best, and that was my case," Kvitova said. "It"s been a long time since I turned a match from match points so this is something special." Also advancing to the next round of the Australian Open warm-up event was Spain"s Paula Badosa, who beat former French Open champion Jelena Ostapenko 7-6(1) 6-1. "A match against Jelena is always tough," said Badosa, who had a breakthrough season in 2021 and captured titles in Belgrade and Indian Wells. "She"s a tough player and you never know how good she can be that day, so I"m really happy with my first win of the year." Seventh seed Ons Jabeur of Tunisia faces local hope Astra Sharma later while Sofia Kenin meets Daria Kasatkina. In the men"s ATP 250 tournament in Sydney, eighth seed David Goffin rolled past Argentina"s Facundo Bagnis 6-4 6-4. Australian Nick Kyrgios, who pulled out of last week"s Melbourne Summer Set tournament due to asthma, withdrew from his clash with Italian seventh seed Fabio Fognini. The Australian Open begins on Jan. 17.