The defending champion, who turned 29, battled through 6-2 6-7 (3/7) 6-2 and will next face either Czech Kristyna Pliskova, sister of fifth seed Karolina Pliskova, or Romanian 27th seed Irina-Camelia Begu.
The prospects looked bleak for the unseeded Witthoeft, who has twice lost to Kerber at Wimbledon including an embarrassing 6-0, 6-0 'double bagel' in 2015.
Witthoeft has never beaten a top 10 opponent but she showed far more fight than at the All England Club, with Kerber taken to three sets for the second match in a row.
She is not only defending a major title for the first time but also playing her maiden Grand Slam as top seed, admitting she is still getting used to dealing with the extra pressure.
Also Read
"To have this pressure is a privilege. It's completely new for me, but I'm doing well. I'm just trying to enjoy it," she said, before the Rod Laver Arena crowd sang "Happy Birthday".
"I am getting older... I think I will have a great day today," Kerber added.
Ranked 89, Witthoeft was pushed around the baseline by the left-hander but some unusually wild shots from Kerber handed her break opportunities, one of which she grabbed to level the match.
It was an aberration with the birthday girl immediately breaking back, before turning up the heat as they traded blows to score another break when Witthoeft whipped a forehand long to go 2-5 down, with Kerber easily holding to take the set.
Bidding to be the first woman to defend her Australian title since Victoria Azarenka in 2013, Kerber had an indifferent lead-up to Melbourne with early exits in Brisbane and Sydney this month.
She came out firing in the second set, ambushing Witthoeft for an early 2-0 lead. But she lost focus and her countrywoman made the most of it, breaking back with some pinpoint shots from the baseline.
The set turned into a slug-fest and Kerber succumbed to the pressure in the tiebreak, firing blanks on her serve which allowed Witthoeft to win six points in row and take the set.
Disclaimer: No Business Standard Journalist was involved in creation of this content