Now 18th in the world, Wozniacki was beaten 1-6 7-6 6-4 by a player 58 places below her in the rankings.
"I would say it's a pretty s***** start to the season," the Dane told reporters. "It wasn't a pretty first set but I got it done and really should have closed it off in two.
"I let her back into the match, and it was basically my own fault that I'm not here as the winner."
Wozniacki's record at Melbourne Park has got progressively worse since 2011 with her record reading semifinals, quarterfinals, fourth round, third round, second round -- and now this first-round exit.
Williams showed her good friend how it should be done with a 6-4 7-5 win over Italy's Giorgi.
Ahead of the Australian Open's start, the focus had been on Williams' nagging knee injury, but the 34-year-old American, who is one behind Steffi Graf's record of 22 grand slams, said she "didn't feel it all" in a match that lasted an hour and 43 minutes.
"I think I served well today," added Williams. "I got broken once, but other than that, I was able to stay focused on that part. And I was able to serve really well and that really helped me."
Serene for Sharapova
Elsewhere, Maria Sharapova, who lost out to Williams in last year's final, eased to a 6-1 6-3 win over Japan's Nao Hibino.
Seeded fifth, Sharapova won the tournament back in 2008 and was pleased with her start to her campaign.
"I haven't played many matches in many weeks so it's great to come out here and start my season at the Australian Open," she said.
"I was quite pleased in the way I was able to play in my opening match. I'm feeling really good, which is a positive. I'm just happy to finish off today and be able to get ready for the next one."
While Sharapova comfortably progressed, other seeds fell by the wayside.
Italy's Sara Errani, the 17th seed, was beaten 1-6 7-5 6-1 by 21-year-old Russian Margarita Gasparyan.
Sloane Stephens, the 24th seed, also suffered disappointment as she lost out to Chinese qualifier Wang Qiang 6-3 6-3.
No problems for Novak
Novak Djokovic cruised through the opening round by defeating South Korea's Hyeon Chung 6-3 6-2 6-4.
The reigning champion and world No.1 is attempting to equal Australian Roy Emerson's record of six Australian Open crowns.
"This court is probably my most successful court in my career," said Djokovic. "I've had some memorable moments, played some big matches here, so it's great to be back.
"Last year has been a remarkable season and I enjoyed it very much. I didn't lose too many matches.
"I tried to stay healthy and stay consistent on all surfaces because each year starts here in Australia.
"I started this season very well in Doha and hopefully I can have a great start here in the Australian Open and take it from there."
Roger Federer, the 17-time grand slam champion, eased past Nikoloz Basilashvili 6-2 6-1 6-2 to set up a second round tie against Ukraine's Alexandr Dolgopolov.
Elsewhere, there were wins for home favorite Nick Kyrgios, Kei Nishikori, Tomas Berdych and Jo-Wilfried Tsonga.