Curtoni won the giant slalom at the Trofeo Topolino in 2004 . In December 2006 she competed in her first FIS race . In March 2007 she won the Italian junior championships in slalom and downhill. Shortly before, she had contested her first European Cup race and participated in the European Youth Olympic Festival in Jaca , where she was 13th in the giant slalom. The next appearances in the European Cup followed in January 2008 and at the beginning of the 2008/09 season she won her first points with 26th place in the giant slalom in Funäsdalen . In March 2008 she was again Italian junior champion in slalom. At the Junior World Championships in 2008 in Formigal , Curtonis' best result was 24th place in the giant slalom. A year later at the Junior World Championships 2009 in Garmisch-Partenkirchen , she reached the goal in all competitions, which brought her third place in the combined ranking; her best individual result was eleventh place in the slalom. At the 2010 Junior World Championship in the Mont Blanc region , she also finished in all races. The best results were eighth place in the slalom and ninth place in the downhill, also in the combined classification it was enough for ninth place.
In the European Cup, Curtoni made it to the top in the 2009/10 season . After she had never finished in the top ten before, she celebrated her first victory on January 11, 2010 in the super combined of Caspoggio . That winter, she also won the super combination class. In the Downhill and Super-G disciplines, she had another five podium places by the end of the season, placing her second in the Super-G classification and third in the overall classification. She also competed in her first two World Cup races , but remained without points (no ranking among the top 30).
Curtoni has regularly competed in the World Cup since the 2010/11 season . She won her first World Cup points on December 19, 2010 with 23rd place in the super combined of Val-d'Isère . In the following month she reached her first top 10 result as tenth in the Super-G of Cortina d'Ampezzo on January 23, 2011. At the Junior World Championship 2011 in Crans-Montana , she won the Super-G. Three days later she reached sixth place in this discipline at the 2011 World Championships in Garmisch-Partenkirchen . She achieved her best World Cup result so far on February 5, 2012 with fifth place in the Super-G in Garmisch-Partenkirchen. In the 2011/12 season she finished eleventh in the Super G World Cup with a total of five top 15 results in this discipline.
On March 16, 2016 Curtoni achieved her first World Cup podium finish with third place in the downhill from St. Moritz . During the giant slalom training on November 17, 2017 in Copper Mountain , she tore a cruciate ligament in her right knee, which meant that she was canceled for the 2017/18 season, which she started with 27th in Sölden . She achieved her first World Cup victory on January 25, 2020 in the downhill from Bansko .