Kerber, ranked No. 6 in the world and seventh seeded in Melbourne, denied the American from equaling Steffi Graf's Open-era record of 22 Grand Slam singles titles.
Kerber, a 28-year-old left-hander, was playing the first Grand Slam final of her career and Williams had won the pair's last four meetings, all of them in straight sets.
Kerber was solid in the first set, drawing 23 unforced errors from Williams and breaking twice. Williams rebounded, powering to a 4-1 lead in the second set to push the match to a third.
Kerber built a 2-0 lead in the third set and raced out to a 5-2 lead. The No.1-seeded Williams nearly caught up again -- she won the next two games and was a point away from 5-all -- but Kerber finally closed out the match that took two hours, eight minutes.
Williams overshot a forehand volley on match point, sending Kerber sprawling to the ground in tears.
"I got my second chance, and this is my dream come true," said Kerber, who joins Graf as the only German women to win a Grand Slam title in the Open era. "My whole life I am working really hard, and now I am here and call myself a Grand Slam champion."
"Every time I walk in this room, everyone expects me to win every single match, every single day of my life," Williams said. "As much as I would like to be a robot, I'm not. I try to. But, you know, I do the best that I can. I try to win every single time I step out there, every single point, but realistically I can't do it. Maybe someone else can, but I wasn't able to do it.
"I think I did the best I could today. Would I give myself an 'A'? No. But today, this is what I could produce today. Maybe tomorrow I could produce something different. But that's all I can go off."
The 34-year-old Williams, who has won six Australian Opens, was first to take the microphone at the trophy ceremony.
"Angie, congratulations. You really deserved it -- let me be the first to congratulate you," Williams said. "I hope you enjoy this moment."
With a big smile on her face, Kerber followed Williams to the podium.
"First of all, I would like to say congratulations to Serena," Kerber said. "You're really an inspiration for so many people and young tennis players. You've created history. You're a champion. You're also an unbelievably great person. So congratulations to everything you've already done."
Two weeks ago, Kerber came within one point of exiting the Australian Open in the opening round. Six matches later, she can call herself a Grand Slam champion.
"When I was match point down, I actually had one leg in the plane back to Germany," Kerber said. "I got a second chance, and I took that chance to be here in the finals to play against Serena. I'm really honored to be in this final and to win it -- my dream came true tonight.
"My whole life I was working really hard, and now I'm here, and I can say I'm a Grand Slam champion, and it sounds really crazy. These have been the best two weeks of my life."