The Romanian top seed defeated Williams 6-2, 6-3 in one hour 17 minutes to post her best performance so far at this year's tournament after struggling through the early rounds.
The two-time Grand Slam winner, seeded 18, defeated Timea Bacsinszky of Switzerland 7-6 (7/5), 6-2 to make the fourth round at Melbourne Park.
Williams swatted aside Ukrainian teenager Dayana Yastremska 6-2, 6-1 in a Melbourne Park mauling that reduced the world number 57 to tears.
The Russian 15th seed breezed past seasoned Belgium David Goffin 6-2, 7-6 (7/3), 6-3 in two hours on Melbourne Arena.
On day six at Melbourne Park, the 23-time Grand Slam winner crushed Ukrainian teenager Dayana Yastremska 6-2, 6-1 before consoling her at the net as she burst into tears.
The 2018 finalist will face 22nd seed Roberto Bautista Agut for a place in the quarterfinals.
Nadal will face unseeded Czech former world number four Tomas Berdych for a place in the quarterfinals.
The defending champion lost to Maria Sharapova in three sets.
The Swiss ace has won the last two tournaments at Melbourne Park in a late-career resurgence.
Tomas Berdych rallied to beat Argentine 18th seed Diego Schwartzman.
Seventh seed Dominic Thiem limped out when he retired while losing 7-5, 6-4, 2-0 to young Australian wildcard Alexei Popyrin.
The veteran two-time Grand Slam champion said the firebrand player would never again feature in Davis Cup while he captained the Australian team.
The American won 6-2, 6-2 in 70 minutes, setting up unseeded Ukrainian teenager Dayana Yastremska as the next hurdle in her bid for another major to equal the mark set by Australian great Margaret Court.
The Romanian top seed eventually downed the American 6-3, 6-7 (5/7), 6-4 after two-and-a-half hours in another unconvincing display after also struggling in her opening match.
The 19-year-old Australian number one De Minaur went to primary school in Spain, has a Spanish mother and a Uruguayan father and speaks fluent Spanish.