It was Federer's second lopsided win over Bjorkman in the past three Grand Slam tournaments. He beat the 34-year-old Swede in straight sets in the Wimbledon semifinals last year as a warmup to beating Rafael Nadal in the final.
Bjorkman relied on drops and some improvised shotmaking to move Federer around, but it rarely worked consistently in the match that lasted 1 hour, 35 minutes.
Federer maintained his record of never dropping a set against Bjorkman.
"Jonas is a great guy, he always puts up a good fight," said Federer, who is chasing a 10th Grand Slam title. "Today it went my way, I'm playing pretty well right now."
The heat that forced dozens of matches to be delayed until after sundown on Tuesday, had relented by Wednesday morning in Australia, with matches on all courts starting on time in temperatures around 90 degrees.
It was about 10 degrees cooler in overcast conditions 2 hours later when the Federer-Bjorkman matched began.
Former U.S. Open women's champion Svetlana Kuznetsova, the No. 3 seed, beat Monique Adamczak of Australia 6-2, 6-1 in the first match at Rod Laver Arena, where the roof was reopened after being closed for all but one match Tuesday.
Jelena Jankovic continued her solid start to the year. The No. 11 seed followed up a title and a finals appearance by advancing to the third round here with a 6-2, 6-2 victory over Virginia Ruano Pascual.
The 12 women's first-round matches held over from Tuesday were completed early Wednesday, with No. 8 Patty Schnyder, No. 9 Dinara Safina, No. 15 Daniela Hantuchova, No. 17 Anna-Lena Groenefeld and No. 19 Li Na of China all advancing.
In earlier action, fifth-seeded American James Blake withstood a first-set tiebreaker on Tuesday, then pulled away for a 7-6 (8), 6-2, 6-4 victory over Moya, who he defeated in the final of the Sydney International last weekend.
"I was lucky to get through that," Blake said of his Sydney win. "And he's definitely not the guy I wanted to see in the first round here. But I felt great tonight."
Blake said it was "pretty strange" for the two players to be across the net from each other twice in four days.
"I think that's part of the reason I was so excited at the end of the match," Blake said. "I know it's a tough situation.
After he lost (in Sydney), a lot of the pressure is off him. He can come in here and just feel like he can go after his shots a little more, be a little more aggressive, have really nothing to lose."
Blake knows that feeling. It has been a steady climb back in the rankings since 2004. He fractured vertebrae in his neck, lost his father to cancer and contracted a shingles-like condition that affects hearing, sight and caused paralysis on one side of his face.
He finished that year at No. 94 - but moved to No. 24 at the end of 2005 and No. 4 at the end of last year.
"I think my best is a lot better than two years ago," Blake said. "That's basically the validation that I've accomplished my goal."
In the second round, Blake will face compatriot Alex Kuznetsov, who beat Australia's Peter Luczak 6-4, 5-7, 6-7 (5), 6-1, 6-4.