The fourth seed defied a Melbourne Park heatwave to run out a comfortable winner in 71 minutes in roasting sunshine.
The impressive 24-year-old will play either 13th-seed Linda Noskova of the Czech Republic or China's Wang Xinyu for a place in the quarter-finals.
Anisimova enjoyed a breakout year in 2025, reaching finals at Wimbledon and the US Open, and is aiming to go one better in 2026
"Super-hot today," Anisimova said in her on-court interview, which she conducted wrapped in an ice towel.
"I had a lot of fun today playing in front of you guys, especially a lot of American supporters."
Anisimova steamrollered the 68th-ranked Stearns in the first set at Margaret Court Arena.
The 24-year-old Stearns held up the victory charge in the second set as Anisimova wobbled on her serve.
The world number four looked briefly rattled as Stearns won three games in a row after trailing 5-1.
It only delayed the inevitable, but not before Anisimova racked up a seventh double fault.
"We were just battling it out there at the end," said Anisimova, who is yet to drop a set in three matches at the first major of the season.
She defeated Switzerland's Simona Waltert 6-3, 6-2 in her opener and dismissed Katerina Siniakova 6-1, 6-4 in round two.