2015 photo by Paul Bauman
Federer, seeded No. 3, defeated No. 27 Grigor Dimitrov of Bulgaria 6-4, 3-6 6-1, 6-4 to become the first man with 300 Grand Slam victories.
"It's very exciting, I must tell you," Federer, who will turn 35 in August, said on ausopen.com. "Like when I reached 1,000 (overall match victories) last year, it was a big deal for me. Not something I ever aimed for or looked for, but when it happens, it's very special.
"You look deeper into it, where it's all happened and how. Yeah, so it's very nice. I'm very happy."
A distant second on the list in the Open Era is Jimmy Connors at 233 Grand Slam wins. Federer needs seven more to surpass Martina Navratilova for the overall record, which he should achieve at Wimbledon this summer.
Dimitrov, 24, has been called "Baby Fed" because his talent and playing style are similar to Federer's. Both have sensational one-handed backhands.
Sharapova, the No. 5 seed and 2008 champion, topped Lauren Davis of Boca Raton, Fla., 6-1, 6-7 (5), 6-0 to become the 16th woman with 600 career wins.
"Oh, wow, I've won 600 matches?" Sharapova, 28, mused on ausopen.com. "Oh, boy. Is this like a friendly reminder that I'm getting older?"
2014 photo by Paul Bauman
Daria Gavrilova, who won the doubles title in the 2014 Sacramento Challenger (with fellow Australian Storm Sanders) in her first tournament back from reconstructive ACL surgery, upset a seed for the second straight match.
After knocking off No. 6 Petra Kvitova, the 21-year-old Moscow native edged No. 28 Kristina Mladenovic of France 6-4, 4-6, 11-9.
Gavrilova will face No. 10 Carla Suarez Navarro, who took the doubles crown in the 2014 Bank of the West Classic with fellow Spaniard Garbine Muguruza, for a quarterfinal berth.
In the second round of men's doubles, 13th-seeded Raven Klaasen of South Africa and Rajeev Ram of Carmel, Ind., defeated California natives Steve Johnson and Sam Querrey 3-6, 6-3, 7-6 (4).
Johnson, a Southern Californian who won the 2012 Aptos Challenger, and Querrey, who was born in San Francisco, advanced to the U.S. Open semifinals last September, ousting top seeds and defending champions Bob Bryan and Mike Bryan in the first round.
Klaasen and Ram will face the third-seeded Bryan twins for a berth in the Australian Open quarterfinals.
Querrey, 28, and Ram, who will turn 32 in March, won the doubles title in the now-defunct SAP Open in San Jose with separate partners. Querrey triumphed with now-retired Mardy Fish in 2010, and Ram prevailed with former Stanford All-American Scott Lipsky in 2011.
Ram was the singles runner-up to Wayne Odesnik in the Sacramento Challenger 10 years ago. Odesnik, a 5-foot-11 (1.80-meter) left-hander from Florida, was suspended for 15 years last March for his second doping violation.
Ram also reached the Sacramento doubles final in 2008 with John Isner. They lost to fellow Americans Brian and Dann Battistone.
Brian Battistone employed a unique volleyball-style jump serve, switching his racket hand in mid-air. Both Battistones used a bizarre two-handled racket.