Arena, held court as he swept to a straight-sets win, after coming through a tight second-set tie-break, 6-4, 7-6 (7/5), 6-1.
After Tomic had talked up his chances of an upset, Federer's motivation was clear as he broke immediately and took the first set, clawed his way back from 4-1 down in the second-set tie-break and then sped through the third.
Federer, who became the first man to collect 250 Grand Slam wins, will now face Canada's Milos Raonic in the fourth round as he continues his bid for a fifth Australian Open crown. "Bernard has had a great run and he really got the best out of me tonight, so I hope he can keep it up," Federer said.
Earlier, Williams and defending champion Victoria Azarenka came through their first uncomfortable moments, and Murray was also tested before reaching the last 16 at Melbourne Park.
Williams, eyeing a calendar-year Grand Slam, was broken for the first time in the tournament by Japan's Ayumi Morita, before recovering from 0-3 down in the second set to win 6-1, 6-3. She also unleashed her fastest ever serve, a 207 kilometres per hour (128 mph) bullet which equalled a speed clocked in round two against Garbine Muguruza.
World number one Azarenka screamed at herself and thrashed her racquet before overcoming an unexpectedly stiff challenge by America's Jamie Hampton, who bravely played through severe back pain.
Argentina's Juan Martin Del Potro, seeded six, became the tournament's biggest casualty when the 2009 US Open champion slumped to a five-set defeat to unseeded Frenchman Jeremy Chardy.
Jo-Wilfried Tsonga and Richard Gasquet also went through, and Gilles Simon came through a nearly five-hour, five-set marathon with Gael Monfils as four Frenchmen made the fourth round, equalling the country's best performance.
In the most compelling day so far, Murray extended his Grand Slam winning streak to 10 matches but not before a thorough workout from hitting partner Ricardas Berankis, and he let his frustrations show in the 6-3, 6-4, 7-5 win.
Italy's Andreas Seppi ousted 12th seed Marin Cilic, but Tsonga found it easier with a straight-sets win over Blaz Kavcic, who was on an IV drip just two days ago.
Fruitful day for Indians at Melbourne
It turned to be a good day for India at the Australian Open as Mahesh Bhupathi entered the men's doubles third round while Leander Paes and Rohan Bopanna progressed to the mixed doubles second round with their respective partners.
Bhupathi and his Canadian partner Daniel Nestor, seeded fifth, defeated Romania's Victor Hanescu and Slovak Martin Klizan 6-1 7-6 (8) to enter the third round. They next face unseeded Italian combination of Simone Bolelli and Fabio Fognini, who shocked 12th seeds Rohan Bopanna and Rajeev Ram 6-2 7-6 (3).
Paes and Elena Vesnina overcame a stiff resistance from unseeded team of Pakistan's Aisam-Ul-Haq Qureshi and Sofia Arvidsson of Sweden. The second seeded Indo-Russian pair won 6-7 (8) 6-4 10-7.
Bopanna and Chinese Taipei's Su-Wei Hsieh defeated Australian-American pairing of Ashleigh Barty and Jack Sock 6-3 6-3.