The 30-year-old previously had made 14 semi-final appearances and had pocketed only one silver at the 2015 Nicosia meet, and one bronze at the 2013 Granada meet.
She is the first Thai shooter to win a World Cup gold medal.
The Rio de Janeiro competition served as a test event for the upcoming Olympic Games in Rio.
In the gold medal match, it took a tie-breaking shoot-off for Sutiya to prevail over Rhode after they both finished with 15 target hits. At the fourth additional double Rhode missed, giving Sutiya the chance to shatter the gold medal target, which she did.
“I’ve been in so many finals – I’ve got three silvers – but today being on top of the podium it is the greatest feeling,” she said. “Now I will be in San Marino in June and then I’ll focus on the Olympics.”
She added: “For me, this competition is this competition. The Olympic Games are something different. I’m glad anyway that I did it here in Rio. I did my best and the hard work finally paid off. It was an honour to compete with Kimberly. She’s the Olympic champion and an icon of this sport. I truly respect her.”
In the bronze medal match, China’s Lu Min prevailed over the United States’ Amber English after both were beaten by Sutiya in a three-way shoot-off to determine the second athlete to enter the final.
Lu, competing in her first World Cup finals phase, won 13-12.