The 30-year-old Russian looked like her old dominant self in her first grand slam match since serving a 15-month doping ban, defeating world number two Simona Halep in three entertaining sets.
The five-times grand slam champion fell to her knees after dispatching the Romanian in a match she said she had "no right to win", given her extended absence from the game and her nagging injuries.
Wednesday's match will mark the first meeting between Sharapova and 59th-ranked Babos, who was dispatched by Halep in the third round of last year's U.S. Open for her best-ever finish at a grand slam.
Babos defeated Viktorija Golubic of Switzerland in a marathon 7-5 5-7 7-5 first round match of her own behind her commanding serve and potent groundstrokes.
Assuming her 6-foot 2-inch frame can recover from Monday's classic, the more powerful Sharapova should have the upper hand against the shorter 24-year-old from Hungary.
(Reporting by Rory Carroll; Editing by Christian Radnedge)
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