The No.1-seeded Williams hit 31 winners to 17 unforced errors and never faced a break point.
"It was a little tricky out there," Williams said. "It's good to get through that match. She could be a potentially dangerous opponent. She's really good. So I'm just really happy to finish that one."
Williams improved to 53-1 in Grand Slam first round matches, the only loss coming against Virginie Razzano at the 2012 French Open. She has also won 23 matches in a row now, the second-longest winning streak of her career - she won 34 matches in a row between Miami and Wimbledon last year.
"First of all, Sara is a great player and in the Top 10 for a reason," Goerges said. "But unfortunately for her I played well from beginning to end. This is what I've been working for and hopefully I can stay as consistent as I was today throughout the tournament and throughout the year. That's my goal!"
"I'm really excited," Kumkhum said. "I had nothing to lose and I just tried my best. That's it."
"I really want to know what happened out there," Kvitova said. "Unfortunately I didn't play well. I didn't play my game and what I was really trying to work on all off-season. It was a great off-season and I was really excited to be here, but I probably wanted too much, and then everything just fell down."
Kvitova - who had 40 unforced, including 22 off the forehand - was asked what part of Kumkhum's game she struggled with the most. "I think she played the crosscourt angles really well," she said.
And was it from one of the Thai's sides in particular? "Both," the Czech replied.
All the other seeds in action moved through, including No.4 seed Li Na, who routed Croatian qualifier Ana Konjuh, 62 60; No.9 seed Angelique Kerber, who rebounded from a second set disaster to beat Australian wildcard Jarmila Gajdosova, 63 06 62; No.14 seed Ana Ivanovic, who beat Kiki Bertens, 64 64; No.17 seed Samantha Stosur, who avenged a loss to Klara Zakopalova from three days ago with a 63 64 win; and No.22 seed Ekaterina Makarova, who edged Venus Williams in a thriller, 26 64 64.
Serena Williams was asked about Venus Williams' loss. "It was an extremely tough draw for her," the World No.1 said. "Makarova plays really, really well down here. I think this court really suits her game.
"It was a good match for her, though. She's doing better."