Expectations are much higher this season.
"It's obviously a lot different - I'm not No. 81 any more. And the court's different - it's a different color," Williams told the crowd after her 62-minute match at Rod Laver Arena against wild-card entry Gajdosova, a Slovak who is representing Australia.
Top-seeded Justine Henin, in her first match at Melbourne Park since retiring from the 2006 final against Amelie Mauresmo, won the last six games to beat Aiko Nakamura, 6-2, 6-2, her 29th consecutive win.
Third-seeded Jelena Jankovic saved three match points and needed 3 hours 9 minutes to edge Austria's Tamira Paszek, 2-6, 6-2, 12-10, at Vodafone Arena.
Henin was going through a divorce and skipped the last Australian Open, then came back to win the French and US Opens and the season-ending championship.
In another first-round match, Rhode Island's Jill Craybas defeated Chan Yung-jan, 6-4, 6-2.
At her pretournament news conference, the seventh-seeded Williams said she had not looked at who she was playing first because she was focused on herself.
At 3-0 in the first set, the attitude seemed to be vindicated.
But then she stumbled, dropping her serve on three forehand errors. Instead of moving her feet, she was reaching for balls and surprised by some of the pace coming from the No. 145-ranked Gajdosova.
Williams held to lead, 4-3, then slipped and fell onto her bottom on the new blue Plexicushion surface. She got up, and regained her focus and momentum.
She won the set with consecutive aces and then dropped just one of her last 16 points on serve and made only five unforced errors in the second set.
"Yeah, I'm feeling good," Williams said after she jogged to the net with her left arm raised, index finger outstretched, to meet Gajdosova. "Most of all, I'm enjoying myself."
On the men's side, second-ranked Rafael Nadal, the only player to beat Roger Federer at the last 10 majors - at the last two French Opens - played Viktor Troicki of Serbia in the night match on center court.
Federer starts tomorrow after a disrupted buildup because of a stomach virus.
"Physically I'm fine now, no more issues," Federer said. "I would consider myself 100 percent."
In a match between two former men's finalists, 2003 runner-up Rainer Schuettler beat 2001 runner-up Arnaud Clement, 6-4, 6-2, 6-7 (3-7), 6-4.
