Raducanu had to come from a set down to beat Linda Fruhvirtova 4-6 6-4 6-2, while top seed Gauff had an easier time of it as she dismissed Tatjana Maria 6-4 6-1 on another day interrupted by the rain.
Second seed Sloane Stephens was only able to get through three games before play was suspended in her match against Rebeka Masarova, while fifth seed Wang Xiyu was 5-3 down in the first set against Karolina Muchova when the rain came.
Fourth seed Bernarda Pera is out after her match with Viktoria Kuzmova resumed having being washed out on Monday, and the American was unable to prevent a 6-4 6-4 defeat, with Kuzmova advancing to face Raducanu in the last 16.
The only two other matches completed on Wednesday (AEDT) saw Elena-Gabriela Ruse beat Erin Routliffe in three sets, and Anna Blinkova overcome Elisabetta Cocciaretto, also in three.
At the Adelaide International, Zheng Qinwen earned a hard-fought victory against number six seed Anett Kontaveit, eventually winning 6-1 4-6 7-6 (9-7).
Eighth seed Ekaterina Alexandrova also crashed out despite winning the first set against Marketa Vondrousova, going on to lose 4-6 6-3 6-2, though seventh seed Jelena Ostapenko is through after beating Karolina Pliskova 6-1 6-3.
In a contest that lasted over two-and-a-half hours despite only two sets being played, Victoria Azarenka beat Anhelina Kalinina 7-6 (11-9) 7-6 (7-5), and will face Zheng next, while Sorana Cirstea will go up against top seed Ons Jabeur in the last 16 after beating Viktorija Golubic in straight sets.