Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
Having passed her earlier tests against more accomplished players, Williams had far too many weapons for the 92nd-ranked Gibbs, who appeared overawed by the occasion on 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.
Williams next faces Czech 16th seed Barbora Strycova for a place in the quarter-finals.