Gauff finds rhythm to breeze into Australian Open second round
The American, bidding to become the first woman since Naomi Osaka in 2018-19 to win the US Open and Australian Open back-to-back, made a nervy start.
But she still had too much for her struggling Slovakian opponent, who failed to win any of her seven service games.
Fourth seed Gauff broke Schmiedlova, ranked 68, four times in the opening set with two holds proving decisive for the 19-year-old, who defended her Auckland title earlier this month.
She found more of a rhythm in the second set, taking it 6-0 in just 25 minutes on a sun-baked Rod Laver Arena.
"I was a little nervous in the first set and I think I did well returning and then I found my serve towards the end (of the set)," she said.
The teenager said she was always nervous in the first round of a major, adding that she had to give herself a talking-to on court.
She said she told herself: "'I feel good, I look good so just have fun.' I was able to relax."
Gauff will play unseeded American Caroline Dolehide in the second round.