Forty year-old Kurten now jumps to third place in the Rolex World Cup Jumping rankings, and won 37,000 euro in prize money at the weekend.
The two Irish riders were amongst nine who qualified for the jump-off from an international starting field of 39.
Afterwards, a delighted Kurten said: "It was great sport here today, and a very fast jump-off. This horse is really a dream, and I'm thrilled with her. I believe this is her sixth World Cup win."
Team Ireland Equestrian show jumping manager Robert Splaine said: "This is an outstanding win for Jessica and Libertina. Both horse and rider are real winners. They are a superstar combination."
He also complimented Dermott Lennon for his third place.
"For a small country to have two riders in the top three in a world cup class is phenomenal," he added.
It was Lennon who showed the way with a win for Ireland in the first competition during the opening day of Gothenburg's five star show in Sweden.
However Kurten also featured in the following competition with a third place on Lady Georgina Forbes' French-bred 'Miribel d'Auvray'.
Co Down-based Lennon and Allan Davidson's mare 'Tolett' were third last to go in the day's two-phase competition, and scorched home almost a second ahead of Swedish challenger Niklas Arvidsson.
With a top class international field lining out for Friday's big jump-off class at Gothenburg, both Kurten, who claimed the runner-up spot on 'Castle Forbes Libertina' and Lennon made the top ten.
The competition, a qualifier for Sunday's World Cup class at the five-star show, saw nine combinations make it through to the second round from a startlist of 46, with 40 year-old Dermott Lennon and Woods Rosbotham's gelding 'Hallmark Elite' edged out by a single time fault and settling for tenth overall.
Despite a blistering finish, Kurten had to give way to local hero Rolf-Goran Bengsston, whose 'Ninja la Silla' stopped the clock just a fifth of a second faster than the Irishwoman, and claimed the 13,000 euro first prize.