The American, seeking to equal Steffi Graf's Open-era record of 22 Grand Slam titles, has also been struggling with a knee injury in the build-up.
But the 33-year-old world number one came through a testing match unscathed.
Sixth seed Petra Kvitova beat Luksika Kumkhum 6-3 6-1 on a scorching day.
The two-time Wimbledon champion has also had problems, with a stomach virus forcing her out of two warm-up events.
"I'm very pleased how I played and how I handled the nerves and everything else," said the Czech. "I had an interrupted lead-up and lost some weight but I'm feeling much better now."
Italy's Sara Errani, the 17th seed, had injury problems during her match and became the first women's seed knocked out, losing 1-6 7-5 6-1 to 21-year-old Russian Margarita Gasparyan.
Defending champion Serena Williams reached the second round of the Australian Open with a tense 6-4 7-5 win over Italian Camila Giorgi in her first tour match in four months.