Hector was second after the opening run but overtook defending overall champion Petra Vlhova for her second straight GS victory.
The Swedish skier let out a scream after crossing the line 0.15 seconds ahead of Vlhova on a clear and cold day at Kronplatz mountain in the Dolomites.
Hector leads the standings ahead of Worley by 95 points.
The giant slalom opens the women's skiing program in China on Feb. 7.
Shiffrin also lost ground in the overall standings. The American's lead over Vlhova was cut to only 17 points.
The women's World Cup circuit moves this weekend to Garmisch-Partenkirchen, Germany -- where a downhill and super-G are scheduled -- before a pause for the Olympics.