It was a close race with the Vernon, B.C. native finishing just behind Sochi Olympic silver medalist Nikolay Olyunin of Russia and the winner of the event, Lucas Eguibar of Spain.
Hill, an X-Games medalist, captured silver last month at the world championships in Kreishburg, Austria.
Fellow Canadian Baptiste Brochu finished 15th
On the women's side, Michela Moioli of Italy won the event continuing her comeback from a serious knee injury she sustained in the Olympic final 13 months ago.
The 19-year-old Italian also took bronze at the worlds in Kreischberg, Austria.
Moioli led the final throughout and finished ahead of two French racers, Nelly Moenne Loccoz and Chloe Trespeuch.
Canadian Dominique Maltais came close to the podium, finishing just off in fourth place.
Veysonnaz hosts another World Cup event Sunday and the season concludes next weekend at La Molina, Spain.