Ko was the youngest woman to win a major when she won the Evian Championship at the age of 18 in 2015.
She followed that with victory in what is now the Chevron Championship in 2016 but, despite having 11 top-10 finishes in the majors since then, she had been unable to add to her tally.
And her hopes of doing so on Sunday were in the balance during an intriguing finale with rain and wind battering the Old Course, as it has done all weekend.
World number one Nelly Korda looked to have wrestled control with a run of three birdies in four holes around the turn, and she led by two on the 14th tee.
But a couple of poor wedge shots around the green led to her taking seven shots on the par-five hole and she then bogeyed the 17th as she faded to finish alongside Vu, Ruoning Yin and Jiyai Shin in joint second on five under.
Meanwhile, Ko, who was playing in a group ahead, made a terrific up and down for par from the back of 16 and then played a delightful second to the 17th, which set up a straightforward par to stay at six under.
Her birdie on the last set the target at seven under and she watched from the practice putting green as Vu failed to match her three.
When asked where she would rank this victory, she replied: “That’s like asking me who I like best, my mum or dad.”
More to follow.
