The top-seeded German who held the top WTA spot in 2016 before Serena Williams took it back in September, could regain the number one ranking.
The top-seeded German who held the top WTA spot in 2016 before Serena Williams took it back in September, could regain the number one ranking were she to win the Gulf event on Saturday.
Kerber's victory also provided revenge against Puerto Rican Puig, who beat the 29-year-old for the Rio Olympic gold medal in August.
Kerber improved to 3-1 in the series with her comfortable win over the number 42 seed at the Aviation club.
"I was trying to play my game. I'm really happy about how I played today," Kerber said. "I was really trying to stay focused on every single point and trying to move well, bringing a lot of balls back.
"I was just thinking about my game, about my rhythm, and not thinking too much about my opponent tonight."
The German will next line up against Ana Konjuh, who eliminated eighth seed Elena Vesnina 3-6, 6-4, 7-6 (7/4).
Seventh seed Elina Svitolina outlasted Christina McHale 4-6, 6-4, 6-3 in a match which went for almost two and a half hours.
"I was fighting myself today, I was not there for important points," the Ukrainian winner admitted. "I didn't do my best, but then I'm really happy that I won.
"This shows I can go through some tough matches even not playing well and then try to find my game, At the end of third set, I found it. It's positive that I fought to the end and didn't give up."
Elsewhere in the third round, American Lauren Davis beat Ekaterina Makarova 4-6, 6-1, 6-3, China's Wang Qiang defeated Kristina Mladenovic 6-1, 6-4 a day after the Frenchwoman had stunned second seed Karolina Pliskova while Anastasija Sevastova defeated Peng Shuai 6-4, 6-3.
American Catherine Bellis sprang a shock on 2012 champion Agnieszka Radwanska upsetting the Polish fourth seed 6-4, 2-6, 6-2 with the 17-year-old earning her first win over a top 10 player.
"It's one of the best feelings in my life, for sure. I'm really happy about the outcome tonight," the Californian said.
"It feels really good. I think I'm definitely playing some of my best tennis right now. It's definitely obviously the biggest win of my career, and probably one of the best days of my life."
Danish tenth seed Caroline Wozniacki needed treatment on a leg at the start of the third set, but carried on to defeat Kateryna Bondarenko 3-6, 6-2, 6-3 after more than two hours of battle.