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Barthel was matching her rival early on in the opener, but the momentum changed in the fifth game when Kvitova took advantage of some poor serving from the German to break for the first time.
Kvitova managed to break once more in Barthel's next service game, before easing to a comfortable success in the first set.
Falling behind hurt Barthel's chances, and there seemed to be little way back for the underdog when she was broken in each of her first three service games in the second set.
Barthel briefly threatened to keep the match going on for slightly longer with a couple of break points, but Kvitova fought back in the sixth game to complete the win with a fifth match point.
The 2011 champion will meet Venus Williams in round three.