There was little to separate the two players, both of which were aiming to reach the fourth round in Melbourne for the first time in their careers.
Kerber, who won Grand Slam titles in 2016 in Australia and the US Open and again at Wimbledon previous year, beat Birrell 6-1, 6-0 on the day she turned 31.
Barty, with the home crowd spurring her on, fed off Sakkari's inconsistency to clinch the crucial first break of the second set as more intelligent play saw her race clear and finish the job in style.
Now Wozniacki is seeded third here and Sharapova is 30th. "To me, she's someone I can relate to because I believe she's become a better player because she plays doubles", tennis legend John McEnroe said on the Channel 9 coverage of Barty.
He'll next play either six-time Australian titlist Roger Federer or American Taylor Fritz, who were playing on Rod Laver Arena around the same time.
Barty thundered down 13 aces and dropped serve just once, but looked ginger at times with her movement, no doubt the result of a gruelling workload of eight matches in the past 12 days. Barty was first to break though - and later the first to reach set point with a break chance at 5-4.
The Greek was unable to hold in her next service game, with Barty converting on a break point to claim the first set in 50 minutes.
"I like her (Barty) in a lot of ways, she plays with a lot of energy".
She showed she's ready to be a Grand Slam factor once again.
Tsitsipas, who is set to have a souvlaki named after him by a Melbourne restaurant following his progression to the fourth round, got past the hard 19th seed Nikoloz Basilashvili 6-3, 3-6, 7-6 (9-7), 6-4 on Margaret Court Arena. Another American woman, 35th-ranked Danielle Collins, joined Anisimova in earning a debut trip to the round of 16 at a major with a 6-3, 6-2 victory over No. 19 Caroline Garcia.
Federer said he was looking forward to playing Tsitsipas in what will be their first head-to-head meeting on the ATP Tour, although they did face each other at the Hopman Cup earlier this month.
Taking everything into consideration, I am going to pick Maria Sharapova to win this match. "All the ones that kind of, not didn't fit anymore, but Mum has a cabinet at home she keeps them all in, and it was kind of a bit of a tradition every year that we gave a few to Jim and Robby at West Brisbane Tennis Centre and they filtered through to the fixtures, with the young kids".