Robinson, who won two successive giant slaloms and a Super-G in November and December and led the standings last month, slipped to third overall in the discipline.
Meanwhile, Wānaka's Finley Melville Ives came second in his Freeski World Cup event in Calgary on Saturday.
Switzerland's Camille Rast went on to win the World Cup Alpine event for the first time in her career in Slovenia on Saturday - a little over a month before the Milano Cortina Olympics.
The 26-year-old reigning slalom world champion took her third World Cup win - after two slaloms last season - by setting the pace in the first run down Kranjska Gora's Podkoren piste.
She followed it up, as the last skier down the mountain, with the third quickest time in the second run to win and end a sequence of three second places in her last three races.
Rast raced, as did her teammates, with a black armband in mourning for the victims of a New Year's Eve bar fire in the Swiss resort of Crans-Montana that killed at least 40 people.
Austria's Julia Scheib was second, with a combined time 0.20 slower, and Paula Moltzan of the United States completed the podium.
Scheib, with three wins and two second places in giant slalom so far this season, leads Rast in the standings by 119 points.
US great Mikaela Shiffrin finished fifth, behind Sweden's Sara Hector, with Italian-born Albanian Lara Colturi sixth.
Rast's win was the first in Kranjska Gora by a Swiss female skier since Vreni Schneider in 1991.
The women have a slalom on the same Slovenian piste on Sunday, with Shiffrin chasing her seventh successive win in the discipline and sixth this season.
