The world No 14, who beat defending champion Maria Sharapova on Thursday, will next meet unseeded American Madison Brengle.
Russian Makarova started well and went 3-0 up but Kerber roared back, taking the ball early and attacking at every opportunity to win the next seven games while her opponent littered the indoor arena with unforced errors.
“I am kind of speechless. It’s just amazing to be on centre court,” said the unseeded Kerber who had a bad start to the year but won a tournament in Charleston, South Carolina earlier this month.
“I have rediscovered my joy and passion for tennis and I am enjoying every minute.”
Brengle, 25, had to battle back from a set down to beat Caroline Garcia of France 3-6 6-3 6-3.
World No 3 Simona Halep eased past Sara Errani of Italy 6-4 6-4 as the Romanian set up a meeting with former No 1 Caroline Wozniacki.
Dane Wozniacki had an even easier task, crushing eighth seed Carla Suarez Navarro of Spain 6-0 6-3.?? ??