At 36, Williams is the oldest woman in the singles draw at Melbourne Park and seeded 13th for her open era record-extending 73rd appearance at a grand slam.
Like sister Serena, she rested up for the last couple of months of 2016 before returning at the Auckland Classic two weeks ago.
The American could quite easily have put the loss of her opening service game on Monday down to rustiness but instead gave credit to 22-year-old world number 101 Kozlova.
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"She played amazing," Williams said. "Hardly any errors, she played amazing defence. She didn't make it easy, so it's really satisfying to get past a player who's on fire."
When asked how she managed to keep beating players so much younger than herself - Kozlova was born the year Williams turned professional - the seven-times grand slam champion assumed the role of elder stateswoman.
"Well I know how to play tennis ... You know, I like to think I’m good at this," she said.
"She hasn't had the years that I've had yet. Se hasn't had the grey hairs that I'm dying, the wrinkles that I'm hiding. You're trying to make me feel old now!"
Williams next faces Swiss qualifier Stefanie Voegele, 26, or Japan's Kurumi Nara, 25, as she bids to go deeper into a tournament where her best finish was a run to the final in 2003.
"I'm always ready," she said. "2017 is going to be a wonderful year, and it's been a wonderful start with this win and I couldn't ask for any more - except a win in the second round, and third and so on."
Williams has not won a grand slam title since claiming her fifth Wimbledon crown in 2008 but said she still embarked on every tournament with the intention of winning it.
"I've not come all the way to Australia for kicks and giggles, I'm here to be competitive," she said.
"Each player in the draw has an unbelievable ability to play tennis. There are some that have won more championships than others, but it's because we know how to play this game, and it's pretty serious stuff for us."
(Editing by Peter Rutherford)
