The Belarusian 24-year-old is hoping her victory at the exhibition match in the resort town will set the stage for a strong performance at the upcoming Australian Open.
"It's a great warmup before going to compete and start the year," she told reporters. "It's always really fun because we take each other to the limit."
Asked whether the pair would meet again in the Australian Open final, she replied: "That's what we're going to really work hard for."
A jet-lagged Williams, who arrived in the kingdom a day later than Azarenka, shrugged off her defeat.
"We had a really good match. We had a lot of moving and I think it was a really good warm up for us in the future," she said, making her debut in Hua Hin.
2013 was mostly a year to forget for Azarenka who won just three titles against 11 for Williams.Azarenka limped out of Wimbledon in the early stages with a knee injury and failed to reach the WTA Championships semi-finals in Turkey in October as she battled a lower back injury.
A month earlier she crashed out of the China Open in the first round.
In contrast, Williams enjoyed a match record of 78 wins against just four defeats, claimed the season-ending WTA Championships title and became the oldest number one player.
Azarenka will start her 2014 season with a return to Australia where she was forced to withdraw from the semi-finals a year earlier due to a toe infection on her right foot.