Top seed Williams put her nervy first-round three-set victory behind her to crush Els Callens of Belgium 6-4, 6-0 while third seed Safin saw off Spain's Albert Montanes 6-3, 4-6, 6-4, 6-1.
Men's top seed Lleyton Hewitt clashes with fellow Australian Todd Larkham in the night session at Melbourne Park later on Thursday.
Safin, runner-up in the Australian Open last year, continued his return to fitness after pulling out of last week's Sydney International with a shoulder injury and did enough to muscle his way into round three.
The Russian plays Rainer Schuettler next.
The number 31 seed from Germany knocked out former Wimbledon champion Richard Krajicek of the Netherlands 6-3, 7-5, 6-4.
Williams produced a vastly improved performance to beat the Belgian on centre court. She had been hesitant and nervous against Frenchwoman Emilie Loit in the opening round.
On Thursday she was as decisive and overpowering as ever, although she did admit to feeling a little tense as she looks to win the only grand slam not in her possession.
"Maybe I'm putting a little too much pressure on myself," Williams said.
"As the match wore on, I think I just calmed down... and I realised, for my future matches, that this isn't everything and things could be worse."
The world number one is bidding to become only the fifth woman in history to hold all four grand slam titles at the same time after winning last year's French Open, Wimbledon and US Open championships.
Wimbledon runner-up David Nalbandian of Argentina, seeded 10th, ended Australian Jaymon Crabb's hopes 6-1, 7-6, 6-3 while 18th seed Younes El Aynaoui of Morocco beat the last remaining Asian in the draw, Uzbek Vadim Kutsenko, 6-2, 6-1, 6-4.
James Blake continued his safe passage through the draw, the 23rd-seeded American putting out Argentine Jose Acasuso 6-1, 6-4, 6-4.
In women's action, 25th-seeded American Meghann Shaughnessy trounced Slovak Ludmila Cervanova 6-1, 6-1 and 16th-seeded Frenchwoman Nathalie Dechy beat Czech Daja Bedanova 6-3, 6-3.
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