The Czech got off to a perfect start by breaking Diyas in the first game of the match, although the world number 86 fought back and restored parity in the fourth game.
Kvitova kept pushing for another break of serve, however, and the Kazakhstani's resistance was finally broken in the 11th game. The world number six then successfully served out the opening set to take it 7-5.
Things were more straightforward for Kvitova in the second set as she conceded just five points on her own serve throughout while also breaking Diyas twice to clinch the match.
The Czech will now face Marina Erakovic in the second round.