Olympic silver medallist Aicher finished second in the first of two downhills in Val di Fassa by 0.01 of a second , with world and Olympic champion Breezy Johnson of the United States completing the podium a further 0.28 seconds slower.
It was 28-year-old Pirovano's first World Cup podium finish in her 125th start.
Vonn, recovering from a broken leg in last month's Milano Cortina Olympics after winning two downhills this season at the age of 41, remained leader of the downhill standings with 400 points - 14 clear of Aicher with two races worth a total 200 points still to be won.
Pirovano's first win of the season, with bib number eight, left her third overall and 64 points behind Vonn. Aicher started 11th and Johnson ninth.
The women have another downhill on Saturday and then race at the World Cup finals in Norway on March 21st.
American great Mikaela Shiffrin, who does not compete in downhill, remained top of the overall World Cup standings with a lead of 139 points over Aicher, who could overtake her at the weekend.