The 27-year-old came out on top in the big final, denying home hope Victor Oehling Norberg who placed second with Jean Frederic Chapuis third and Joe Swensson fourth.
That marked Fiva's first World Cup win since round five in Les Contamines in the middle of January and gives him a lead of 140 points with two events left, the first of which is on Sunday in Are.
Swiss teammate Armin Niederer occupies second in the overall men's ski-cross World Cup standings but struggled in the first of two events in Are as he placed 26th overall.
Meanwhile in the ladies' event, Anna Woerner picked up her second World Cup victory of the season as Ophelie David narrowed the lead of another Swiss overall leader Fanny Smith.
German Woerner beat Marielle Berger Sabbatel to victory in the big final while Karolina Riemen took third ahead of Heidi Zacher with David failing to make it past the quarter-finals for tenth overall.
Yet, with Smith failing to finish during qualification on Friday, David, who sits second in the overall World Cup standings, cut the Swiss freestyle skier's lead to 34 points with two races left.
- Sports & Recreation
- Ophelie David