Two-time Wimbledon champion Kvitova, who ended 2021 among the world's top 20 players for the first time since 2016, lost in three sets to her Australian opponent 6-7 (4-7) 7-5 6-2. The victory was Hon's first against a player in the top 40.
Elsewhere, No.3 seed Maria Sakkari saw off Slovenia's Tamara Zidansek 6-2 0-6 6-4, while No.7 seed Elena Rybakina earned a 6-4 1-6 6-1 win over Storm Sanders.
Leylah Fernandez, the 2021 US Open runner-up, also looked comfortable in a straight-sets victory against Ekaterina Alexandrova, easing past the Russian 6-3 6-4. The 19-year-old will face either No.5 seed Iga Swiatek or Daria Saville in the next round.
Heather Watson is out after a 6-4 7-6 (7-5) loss to home favourite Ajla Tomljanovic, while in the doubles event, Japanese pair and No.1 seeds Ena Shibahara and Shuko Aoyama were beaten 6-4 6-2 by Victoria Azarenka and Paula Badosa, who will play against one another in the singles on Tuesday.