Azarenka, who beat four seeded players including French Open champion Li Na to win the Sydney International last week, has only lost eight games at Melbourne Park en route to the round of 16.
The 22-year-old from Belarus will next meet Czech player Iveta Benesova, who beat Russian qualifier Nina Bratchikova 6-1, 6-3.
Barthel was on a 10-match winning run in Australia after capturing her first title at the Hobart International last week as a qualifier.
Barthel hit 20 winners — one more than Azarenka — but she was broken three times and failed to convert three break opportunities, including one when Azarenka was serving for the match.
Azarenka was annoyed that she needed five match points to finish off Barthel and for wasting three challenges.
"I've been playing in the end not brave enough to finish the match ... I had to get a little," angry, Azarenka said.
After being wrong on three challenges, she wasn't able to review a line call in the last game when she really needed it.
"I was wrong three times," she said, "so it's my fault, too."
Defending champion Kim Clijsters was set to play Daniela Hantuchova in a night match on Hisense Arena.
No. 2 Rafael Nadal and No. 3 Roger Federer, with 26 Grand Slam titles between them, play in back-to-back men's matches on Rod Laver Arena.