After winning through qualifying for a second straight week, world No.63 Tomljanovic beat fellow qualifier Taylor Townsend 6-4 3-6 7-5 in their first-round clash on Monday.
The 29-year-old Wimbledon quarter-finalist fell to world No.1 Iga Swiatek in the second round at last week's Toronto tournament and will face another tough task against world No.4 Badosa, who enjoyed a first-round bye.
She lost to the Spanish star at both the Sydney Classic and Australian Open at the start of the year.
Swiatek will take on Sloane Stephens in her first match in Cincinnati after the American easily accounted for France's Alize Cornet 6-1 6-0.
World No.2 Anett Kontaveit will face Tereza Martincova after the Czech qualifier got the better of Nuria Parrizas-Diaz 6-7 (4-7) 6-4 6-3, while world No.3 Maria Sakkari will play Caroline Garcia after the Frenchwoman's 6-3 6-3 win against Petra Martic.
Wimbledon champion Elena Rybakina has now won nine of her past 11 matches after defeating Mayar Sherif 6-3 6-2 in their first round clash.
Last year's surprise US Open runner-up Leylah Fernandez has lost three of her past four matches after falling 6-4 7-5 to Russia's Ekaterina Alexandrova.
Alison Riske continued her march towards the top 20 with a 6-1 7-6 (7-2) win against Sara Sorribes Tormo, while Belarus' Victoria Azarenka knocked off 37-year-old Estonian Kaia Kanepi 6-3 4-6 6-3.
Switzerland's Jil Teichmann came up short in a near three-hour war of attrition against two-time Wimbledon champion Petra Kvitova, losing 7-6 (7-2) 6-7 (6-8) 6-3 while Amanda Anisimova defeated world No.10 Daria Kasatkina 6-4 6-4.
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