The two-time defending champion and the American 13th seed haven't met since a January afternoon last year when they battled in a semifinal at Melbourne Park.
Azarenka won 6-1, 6-4 but called for the trainer while leading 5-4 in the second set, having coughed up five match points on serve in the previous game.
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Stephens gained plenty of momentum from surviving the ninth game, but that disappeared when Azarenka called multiple consecutive timeouts to treat what she called breathing issues related to her back and ribs.
Azarenka's actions drew widespread condemnation but didn't stop her from lifting the Daphne Akhurst Memorial Cup for a second consecutive time days later.
Considering Azarenka is aiming to become the first woman in 15 years to win in Melbourne for a third time in a row, how sweet would it be for Stephens to be the one that denies her that opportunity and, in the process, gain revenge for last year's semifinal shenanigans?
Azarenka has steamrolled through her first three opponents on the way to this tantalizing fourth-round meeting, and since her first-set tie-breaker against Johanna Larsson in the first round has dropped just eight games.
Stephens has had a slightly tougher time of it, and had to fight back from a set down to overcome Croatian Ajla Tomljanovic in the second round, but memories of the 2013 semifinal will surely still be burning in her memory and will ensure a cracking affair.
In other women's action on Monday, third seed Maria Sharapova faces Slovakia's Dominika Cibulkova; fifth seed Agnieszka Radwanska takes on Spanish surprise Garbine Muguruza; and Jelena Jankovic meets Simona Halep.
The men's round of 16 also concludes on Monday. The highlight: 17-time grand slam champion Roger Federer faces Jo-Wilfried Tsonga.
In other men's Monday matches, top seed Rafael Nadal will tackle Japan's Kei Nishikori, Andy Murray will play Stephane Robert and Grigor Dimitrov meets Roberto Bautista Agut.
