The former world number one started strongly by breaking Kvitova's serve at the first time of asking, but her opponent later responded with a double break.
After grabbing a one-set lead, Kvitova took a stronghold of the contest by easing to an early break point in the second set.
The 24-year-old broke Sharapova's serve once again and was able to save three break points in the next game to keep herself on top.
Sharapova continued to struggle on her serve, but she inflicted some trouble on Kvitova by breaking her serve to get her first game on the board.
The second seed was able to hold on to her next service game, but Kvitova eventually wrapped up the contest and put her first round-robin victory on the board.