Having passed her earlier tests against more accomplished players, second seed Williams had far too many weapons for the 92nd-ranked Gibbs, who appeared overawed by the occasion at a sun-drenched Rod Laver Arena.
Williams suffered a brief lapse when serving for the match at 5-2 and was broken for the first time, but she promptly broke back to close out the one-sided contest in just over an hour.
The 35-year-old American, bidding for a record 23rd grand slam title in the professional era and a seventh at Melbourne Park, heads into the second week, and a clash against 16th seed Barbora Strycova, in fine touch.
"I feel like I have been able to do pretty good," Williams told reporters, having had only two tour matches to warm up for the tournament after calling off her season after the U.S. Open last September to deal with a knee injury.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I have been doing the things I have been doing in practice, and hopefully I can build up on this.
"That's all I want to do."
Ominously for Czech Strycova and other Tour rivals, Williams could do a whole lot more.
She landed only half her first serves against Gibbs and racked up 26 unforced errors.
It hardly mattered, as Gibbs's feisty opening salvo early in the first set was quickly subdued by Williams's power hitting.
A former national collegiate champion, the outspoken Gibbs has developed a profile with her commentary on various social issues such as gun control and race, but the 23-year-old had enough problems of her own to deal with against Williams.
She double-faulted meekly to drop serve for a second time and trail 5-1 in the first set, and Williams closed it out in 26 minutes.
Statistically, Gibbs was up against it, with Williams not losing to a player ranked outside the top 50 since a shock loss to Virginie Razzano at Roland Garros in 2012.
Adding to that, Williams has lost only twice in 29 matches against fellow Americans since an injury-hampered quarter-final defeat by Sloane Stephens at Melbourne Park in 2013.
Ever generous in praising opponents after crushing them, Williams said Gibbs did "a great job" and that she had not intimidated.
"The same thing with me when I was growing up," said the former world number one.
"I was in awe and had so much respect for these (top) players. But when I stepped out there, I wanted to see what I can do, all my years of work and how it would stand up against the greatest."
(Editing by Sudipto Ganguly/Peter Rutherford)
