Kvitova, seeded third, dropped the first set against German lucky loser Annika Beck 4-6, but then bounced back to win the next two sets 6-3, 6-3.
The Czech Republic native goes on to face American qualifier Alison Riske in the quarterfinals.
Kerber, however, wasn't as fortunate, succumbing to 2009 runner-up Elena Vesnina of Russia 6-2, 6-4 at the Yale University hard courts.
Meanwhile, Czech Klara Zakopalova bested Puerto Rican qualifier Monica Puig 6-4, 6-1. She'll next face Vesnina in the quarters of the U.S. Open tuneup.