Kerber was broken in the opening game but had no trouble the rest of the way against the 2016 runner-up. She broke back immediately and earned another break in the fourth game to take control of the match. She will next face Italy's Sara Errani.
"I played a solid match," Kerber said. "It's always tough to play against her. You never know what's going to happen. She's always a fighter."
American Catherine Bellis, 18, followed up her quarterfinal appearance in Doha by beating Elise Mertens of Belgium 6-3, 6-3. Bellis, who lost to Simona Halep in Doha, will face Wimbledon champion Garbine Muguruza next.
"I've never played her before. It's definitely going to be a new experience for me," Bellis said. "She's an unbelievable player and has been at the top of the game for a while now. It will be great for me just to see where my game lines up against another one of the top players."