The win meant she qualifies for the semi-finals from the Purple Group in excellent form.
Kenin was called into action in the tournament after Bianca Andreescu had retired injured earlier in the week.
Svitolina dumped out by Krejcikova as another seed tumbles
She will face Belinda Bencic on Saturday, though was pushed hard by Kenin after saving two set points in the final set.
Fifth seed Svitolina beats Li to reach third round
Svitolina fights past teenager Babel in straight sets