The American improved from fifth place, posting the fastest time with an all-attacking run to beat Petra Vlhova by 0.15 seconds.
The Slovakian, who has won five of this season's seven slaloms, leads Shiffrin by 220 points with just two more World Cup slaloms scheduled after the Olympics.
The title went to Katharina Liensberger last season. On Tuesday, the Austrian was 0.79 behind in eighth after the first run and ultimately finished 21st after nearly skiing out at the end of her second run. Canada's Ali Nullmeyer and Switzerland's Wendy Holdener, who shared the third spot after the opening run, both failed to finish their final runs.
The Planai course is an annual stop on the men's circuit. The women last raced at the venue during the world championships in 2013.