Fifth-seeded Kerber won 6-2, 7-5 on Friday to move into the fourth round, further than she's gone in six trips to the Australian Open.
Local organizers brought Kerber a cake onto the court immediately after the match and the crowd at Rod Laver Arena sang "Happy Birthday." She blew out the candles and said thank you to the crowd and to 17-year-old Keys.
"Madison is a great young player and it was very tough," said Kerber, a semifinalist last year at Wimbledon. "So happy I won today on my birthday!"
Kerber will next play No. 19 Ekaterina Makarova of Russia, who advanced after a tough 6-7 (4), 6-3, 6-4 win over 2007 Wimbledon finalist Marion Bartoli.
In the fourth round last year, Makarova beat Serena Williams and was the first of only four women to beat the powerful American in 2012. Kerber was the last.
Fourth-seeded Angieszka Radwanska, meanwhile, won her 12th match in a row with a 6-3, 6-1 victory over Britain's Heather Watson on the second of the show courts at Melbourne Park.
"I'm extremely happy to be playing my best tennis from the beginning of the year," said Radwanska, who won tournaments in Auckland and Sydney before coming to Melbourne. "Hopefully I'll play on the same level the rest of the tournament."
She'll next play 2008 French Open champion Ana Ivanovic, who beat Jelena Jankovic 7-5, 6-3 in a matchup featuring two Serbians who were both former top-ranked players.
Ivanovic surged to a 5-2 lead in the first set but lost the next three games. The 13th-ranked Ivanovic broke Jankovic to pull ahead 6-5 and won the first set with an ace.
The 25-year old Ivanovic had an easier time in the second set, wrapping it up on her second match point.
Sixth-seeded Li Na advanced 6-4, 6-1 over 27th-seeded Sorana Cirstea of Romania to a fourth-round match with No. 18 Julia Goerges, who Zheng Jie 6-3, 1-6, 7-5 .
Li won the 2011 French Open just a few months after reaching at the Australian Open.
After soaring to 106 degrees on day four, the temperature dropped into the mid-70s on Friday, and light rain briefly interrupted play on some courts.
Roger Federer has won four Australian Open titles among his 17 majors, and is ordinarily one of the most popular athletes in Australia.
The only problem is this: His 6-3, 6-4, 6-4 win over Nikolay Davydenko on Thursday night set Federer on course for a third-round match against Bernard Tomic, the last remaining Australian in the men's or women's draws.
The 20-year-old Tomic beat German qualifier Daniel Brands 6-7 (4), 7-5, 7-6 (3), 7-6 (8) in the last afternoon match on the center court at Melbourne Park, keeping his cool on a long, searing day.
Federer praised Tomic's play for the crowd, and later said he won't mind for whom or how loud fans are cheering Saturday.
"I don't think it matters whether he's the last Australian or 10 more," Federer said. "There's always excitement about Aussies playing here. I played him here last year. The crowd was great. I expect something similar. If it's not, if it's totally for him, that's fine, too. I'm always excited when the crowd gets into it."
The day-time temperature got progressively hotter until late afternoon, meaning top-ranked Victoria Azarenka had it slightly easier in her second-round match - a 6-1, 6-0 win over Eleni Daniilidou, Greece - than third-ranked Serena Williams did in the next match on Rod Laver Arena, a 6-2, 6-0 win over Garbine Muguruza of Spain.
There was concern after she hurt her right ankle Tuesday that an injury might ruin Williams' run at a third consecutive major title. She said the ankle didn't bother her as much on Thursday as a split lip, which she did by accidently hitting herself in the face with the racket in the sixth game.
"It's OK," she said. "It's a war wound."
She next plays Ayumi Morita, one of two Japanese women already in the third round. The other, 42-year-old Kimiko Date-Krumm, downed Shahar Peer of Israel 6-2, 7-5.
Other women advancing included former No. 1-ranked Caroline Wozniacki, No. 14 Maria Kirilenko, No. 16 Roberta Vinci, No. 20 Yanina Wickmayer and Elena Vesnina, who beat No. 21-seeded Varvara Lepchenko 6-4, 6-2.
After her singles match, Williams attempted to show there was no serious damage to her ankle by combining with sister Venus in a first-round doubles win later in the afternoon.
That was good preparation for Venus' third-round match against No. 2-ranked Maria Sharapova, one of the highlights of Friday's schedule.
Novak Djokovic resumes his bid for a third consecutive Australian Open title when he takes on Radek Stepanek in the third round in the afternoon. No. 4 David Ferrer plays Marcos Baghdatis in the last match in what should be another late finish.
British teenager Laura Robson ensured that the Day Four program ran into Day Five when she rallied to oust No. 8-seeded Petra Kvitova, the 2011 Wimbledon champion, 2-6, 6-3, 11-9. After coming from a break down in the third set, she missed a chance to serve out the match at 6-5. She made no mistake the second time, in the early hours of Friday.
Robson, who combined with Andy Murray to win an Olympic silver medal in the mixed doubles, will next play 19-year-old American Sloane Stephens, who beat Kristina Mladenovic of France 6-4, 6-3.
Murray, who won the Olympic gold medal in singles and then went on to break a long British drought for British men by winning the U.S. Open, beat Joao Sousa of Portugal 6-2, 6-2, 6-4 to advance to the third round in Australia.
Among the other men advancing were 2009 U.S. Open champion Juan Martin del Potro, 2008 Australian finalist Jo-Wilfried Tsonga and fellow Frenchman Richard Gasquet, No. 13 Milos Raonic of Canada, No. 17 Philipp Kohlschreiber of Germany and No. 21 Andreas Seppi of Italy.