Williams, the defending champion, had no trouble against Kerber, who also lost to the American 6-4, 6-1 in the round-robin at this event last year. Kerber was the only player to beat Williams last year -- in Cincinnati -- after the American's first-round ouster at the French Open.
"Today she was playing unbelievable, and I had actually no chance. I mean, she was serving great and also returning unbelievable," Kerber said. "So I was just giving all I could, but yeah, it's tough to play against Serena like this."
Williams was particularly effective with her backhand return, the shot she also used on her first match point. Kerber, who had two straight double-faults to surrender the first game of the second set, produced another to give Williams three match points.
"Tonight was fine. Always good to get here early, not too early for me, but it's good to get here and feel the conditions. Plus, I have played here before, so I think that helped, "Williams said.
Although she is 32, considered a ripe age in tennis, Williams is enjoying the finest season in her career, having already won 10 titles.
She added the French Open and U.S. Open titles to bring her Grand Slam record to 17 championships and is 74-4 for the year.
"I was a little rusty at the beginning. I think it's a little bit expected after a break, and playing right away against a top player always makes it a little bit difficult," Azarenka said.
Kvitova, a former Wimbledon champion, struggled to close out the match. She had four break points and wasted two match points before winning on a challenge. Radwanska's shot after a rally did not get a call but Kvitova asked for a review and the replay showed that the ball had gone long.
Williams, making her eighth appearance in the event, is looking to become the first player to successfully defend the title since Justine Henin in 2007.
Henin was also the last to win 10 titles in a season, in 2007.
Williams has wrapped up the year-end No. 1 ranking for the third time in her career after 2002 and 2009 and Kerber was impressed by William's performance.
"I think I served very good, but she was returning unbelievable. Actually, she didn't give me a small chance to breathe," Kerber said.
Errani hurt her right calf in the third game of the second set and took a medical timeout to have it treated. Several times after that she seemed to be bothered by the injury and to favor her right leg, although she returned after the medical timeout to break Azarenka's serve to level at 2-2. She did not win another game though.
"In the tiebreaker I felt a pain in my calf on serve," Errani said. "The first set was very tough, very long. I was running a lot."
Errani served for the set three times -- and dropped serve each time as both players produced sloppy play with little rhythm.
Azarenka, the Australian Open champion, managed to hold her serve only once through the first eight games but seized her chance when it came.
She won four straight points in the tiebreaker to take a 5-3 lead, and then faltered when she served her sixth double-fault. But an error by Errani gave Azarenka two set points. Errani then committed a double-fault and Azarenka had the set.
"I think, overall was important to take that first set. It was a big turnaround point," Azarenka said.
Azerenka, who was runner-up in the event in 2011 and a semifinalist last year, finished with eight double-faults but she also had 51 winners for Errani's 28.
Azarenka's win was her first since losing the U.S. Open final to Serena Williams. Azarenka lost both of her opening matches in Tokyo and Beijing, where she had 15 double-faults.
The tournament brings together the top eight players in the world. Third-ranked Maria Sharapova dropped out with a shoulder injury.
The players are split onto two round-robin groups, with the top two finishers from each pool advancing to the semifinals.