It was a tough, nearly two-and-a-half-hour battle that closed 3:6, 6:3, 7:5 for Radwańska. The Pole is now ranked 33rd, while Barthel is seeded 75th.
The match marked the third clash between the two players and a third win for Radwańska.
In the second, round Radwańska will take on either Czech Petra Kvitova or Turkish Cagla Buyukakcay. (aba/vb)