Radwanska, 18, and ranked 126, beat world No. 30 Francesca Schiavone in qualifying. Schiavone would have been the Hobart tournament's fourth or fifth seed, but an administration error forced the Italian player into the qualifying rounds.
Radwanska is the younger sister of world No. 10 Agnieszka Radwanska.
Italy's Flavia Pennetta, the tournament's top-seeded player, takes on Israel's Shahar Peer in a night match Monday.
Two other seeded players lost Monday - Anne Keothavong of Britain beat fifth-seeded Agnes Szavay of Hungary 6-3, 7-5 and Carla Suarez Navarro of Spain defeated third-seeded Anna Chakvetadze of Russia, 7-6 (5), 1-6, 7-5.
Elsewhere in the first round Monday, Frenchwoman Virginie Razzano beat Maria Elena Camerin of Italy 6-1, 6-2, No. 4 seed Zheng Ji of China defeated New Zealand's Marina Erakovic 6-1, 4-6, 6-1 and Mara Santangelo of Italy beat Nicole Vaidisova of the Czech Republic 6-1, 6-1.
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