Skistad won ahead of Swedish Jonna Sundling and World Cup leader Tiril Udnes Weng.
Hedda Østberg Amundsen was the third Norwegian girl in the final. She finished fifth and did a career best in the World Cup.
Julie Myhre made it to the semi-finals, but there she had to end up together with the Swiss star Nadine Fähndrich. Thus the 26-year-old quit. Ane Appelkvist Stenseth did the same.
Anna Svendsen, Mathilde Myhrvold, Hedda Bakkemo, Maria Hartz Melling, Kristine Austgulen Fosnæs, Lotta Udnes Weng, Ingrid Andrea Gulbrandsen were eliminated in the quarter-finals.
All Norwegian athletes at the start progressed from the prologue.
[ Stavås Skistad knuste konkurrentene i sprintprologen i Drammen ]