Last year’s beaten finalist looked at ease as she recorded a routine 6-2 6-1 win over her Australian opponent.
The match lasted less than an hour against an opponent ranked 69th in the world, and second seed Williams was generally happy with her display, but believes she still has a lot left to come.
“I thought I played really well today,” said the American. “I knew she was going to be tough so I had to be ready for the match.
“For me there’s always room for improvement though. I still think I could have returned better, come to the net a little bit more.
“That’s exciting to think I can do better.”
Williams won the Wimbledon title in 2002 and 2003 and has also been runner-up twice, including last year where she was beaten by sister Venus.
But the younger Williams already has an eye on the title, even though she is just three days into the Wimbledon fortnight.
“I should have won more than twice here but I didn’t,” she said. “And hopefully I can rectify that this year.”
One former champion who will not be repeating the feat this time around is Maria Sharapova, who was beaten 6-2 3-6 6-4 by Gisela Dulko on Centre Court.
The Russian, who is still finding her form following a shoulder injury, made a fight of things after dropping the first set but was unable to see off her Argentinian opponent.
It is the second year in succession that Sharapova has crashed out in the second round, and the 22-year-old admitted she made too many mistakes.
“I had so many easy balls and I just made unforced errors from those,” she said.
“I don’t really know if that’s because I haven’t played. When I’ve had those situations before, those balls would be pieces of cake and today they weren’t.”
Dulko, who will play in the third round at SW19 for only the second time in her career, revealed nerves almost got the better of her as the match drew to a conclusion.
“I was very nervous at the end,” she said.
“The last game took forever for me, so I was very relieved after that game.”
Seventh-seeded Russian Vera Zvonareva had few troubles in her second-round meeting with Frenchwoman Mathilde Johansson, claiming a 6-1 6-1 win in one hour and 15 minutes.
Victoria Azarenka of Belarus, the eighth seed, had an even easier time of things on Court Two, claiming a 6-0 6-0 success over Romanian Ioana Raluca Olaru.
Tenth seed Nadia Petrova also progressed with a 6-3 6-2 triumph over Shahar Peer, but there was disappointment for 16th seed Zheng Jie, who was beaten 6-3 7-5 by former world number five Daniela Hantuchova.
There were also victories for seeds Dominika Cibulkova, Virginie Razzano and Sorana Cirstea, although Anastasia Pavlyuchenkova was another second-round casualty, the 31st seed losing out to Italy‘s Roberta Vinci in straight sets.
Elena Dementieva of Russia, the fourth seed, also reached the last 32 with a 6-1 6-3 victory against France’s Aravane Rezai.
Dementieva took the first set comfortably before running into trouble early in the second, however she lifted her performance to gain the anticipated straight-sets win.
Former finalist Marion Bartoli joined her in the third round, defeating Swiss player Timea Bacsinszky 7-5 6-1.
Bartoli, seeded 12th this year, was the surprise runner-up in 2007.