This win kept Kerber as a major title contender in this edition of the tournament.
Maria Sharapova, the 2008 Australian Open victor, hurried through the first set on Rod Laver Arena in 23 minutes before beating No. 14-seeded Anastasija Sevastova 6-1, 7-6 (4).
Sharapova, who missed last year's Australian Open while serving a 15-month ban for a failed doping test, was happy to beat the player who'd ended her run at the U.S. Open last year.
She streaked away with the first set and although 2008 champion Sharapova briefly threatened a fightback after falling behind in the second, it was not to be the Russian's night.
The 17th-seeded Keys, who lost in the U.S. Open final past year to Sloane Stephens, saved three break points serving for the match, finally clinching it on her first match point when Bogdan netted a backhand.
21st seed Angelique Kerber remained unbeaten in 2018 on Saturday after easing past five-time Grand Slam champion Maria Sharapova in a highly impressive performance at the Australian Open.
Women's No. 1 Simona Halep took a longer route - equaling a mark in Melbourne for endurance but signalling, perhaps, that she's closer to a Grand Slam breakthrough. "I'm nearly dead", Halep said of the match which equaled Chanda Rubin's win over Arantxa Shanchez Vicario in 1996 - also 48 games - for the Australian Open record in terms of most games.
Their encounter equalled the Open's record for most games played in a women's match - and also saw some impromptu courtside surgery when the American lost a toenail.
"To be able to get these matches, players that are playing this well, I'm going to face a lot of them this year". "My ankle is, I don't know how it is because I don't feel it anymore!"
The Romanian will meet the victor of Ashleigh Barty and Naomi Osaka for a place in the quarter-finals.
Federer entered the Australian Open previous year under similar circumstances, coming off an extended break for a knee injury, and went on to win the title. The Russian was unable to hurt Kerber, who began to take complete control and who raced to a 5-1 lead.
Sixth seed Karolina Pliskova is also in action, against Lucie Safarova, while eighth seed Caroline Garcia meets unseeded Aliaksandra Sasnovich. The former world No 1 had to drop out of the year's first Slam to go for a hip surgery.
Another unexpected loss at a major had the highly touted Zverev admitting he may have a problem.
Fognini will next play the victor of a later match Saturday between Tomas Berdych and Juan Martin del Potro. Dabrowski and partner Mate Pavic of Croatia defeated Australians Alex Bolt and Lizette Cabrera 6-3, 7-5.