Kuznetsova, who held serve at 2-1 despite facing three break points, fired off more winners than her opponent and lobbed solid groundstrokes from both sides throughout during the first set, but Svitolina was able to take her two breaks down by cracking her second services off consistent forehand shooting from the baseline.
The second set was much rougher for the Russian, who was broken three times on the way to an exactly 20-minute rout.
Svitolina faces Alison Riske in the quarterfinals, after the American eased past home favorite Wang Qiang 6-2, 6-1.
Having reached the semifinals of last year's Wuhan Open, Wang made the best possible start against Riske, breaking the American's serve to love in the very first game.
However, to the disappointment of the many Chinese fans in attendance, that was as good as it got for the Tianjin-born star, who couldn't live with Riske's powerful returns and slumped to a straight-set defeat.
There was an upset in the evening session on center court, as No. 2 seed Karolina Pliskova of the Czech Republic was defeated 6-1, 6-4 by Ukraine's Dayana Yastremka.
An out-of-sorts Pliskova failed to break Yastremka's serve at any point throughout the match, and the Ukrainian served up six aces on her way to a straight sets win.
Yastremka's quarterfinal opponent will be fifth seed Petra Kvitova, with the Czech serving up six aces on her way to a straightforward 6-3, 6-3 win over No. 10 seed Sloane Stephens of the U.S..
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