Former world number one Djokovic, who is chasing a record 25th Grand Slam crown in January in Melbourne, eased to a 6-3, 6-3 victory over wildcard Rinky Hijikata.
The 37-year-old Serb broke Hijikata once in the first set and twice in the second for a comfortable 74-minute win.
Djokovic, now ranked seven in the world, was all business against the young Australian and always looked in control as he set up a second-round clash against fellow veteran Gael Monfils.
"To start the new season with a win is obviously very important," said Djokovic, who is pursuing an unprecedented 11th Australian Open title.
"But Hijikata was really good tonight and he made me work for it."
Australian firebrand Kyrgios lost in three tight sets in his first singles match since June 2023.
Kyrgios went down 7-6 (7/2), 6-7 (4/7), 7-6 (7/3) to Frenchman Giovanni Mpetshi Perricard in almost two and a half hours as serve dominated.
The 2022 Wimbledon finalist Kyrgios, 29, is making his comeback following wrist reconstruction and other injuries over the past couple of years.
Ahead of the Australian Open starting on January 12, big-serving Mpetshi Perricard said Kyrgios had shown enough to suggest that his comeback would be a success.
Kyrgios played and won in the doubles with Djokovic on Monday.
"Playing Nick here wasn't a good match-up for me," the 21-year-old Mpetshi Perricard said, asked about playing Kyrgios in front of his home crowd.
"He did some good things, he played with confidence."
The Frenchman, who has risen from 205 in the world at the start of 2024 to his current ranking of 31, fired down 36 aces.
Women's world number one Sabalenka kickstarted her bid to win the Australian Open for a third consecutive time with a straight-forward win after a sluggish start.
The Belarusian appeared bothered by the high humidity on Pat Rafter Arena in Brisbane, particularly during an error-strewn first set against Renata Zarazua.
But after breaking Mexico's Zarazua at 5-4, the 26-year-old surged through the second set to wrap up the match 6-4, 6-0 in 65 minutes.
"The first match is always a tricky one," Sabalenka said.
"It was a tricky start for me but I'm glad that I closed it out in the first set, and in the second set I felt like whatever I tried to do it would work for me.
"So I'm really happy for the first win of the season."
Sabalenka is bidding to be the first woman since Martina Hingis in 1997-99 to win three Australian Opens in succession.
She will play Yulia Putintseva next after the Kazakh's 6-2, 7-5 win over American Mccartney Kessler.
