Kerber, who began last year at the top of the rankings before finishing at No. 22, won her seventh straight match of 2018, including four singles at the Hopman Cup last week.
“This start is not bad, for sure,” Kerber said.
In men’s quarterfinals, fourth-seeded Fabio Fognini beat No. 5 Adrian Mannarino 6-7 (4), 7-6 (4), 6-2, Daniil Medvedev defeated Paolo Lorenzi 6-3, 6-3, and Benoit Paire beat second-seeded Gilles Muller 6-4, 6-4.