The victory in the first super-G since the Winter Olympics was the third of the season for Aicher, a double silver medallist in Cortina, and her second in super-G.
Robinson was 0.88 slower, and Switzerland's Corinne Suter, winner of a downhill on Friday in Soldeu, was third.
Goggia, who finished sixth, stayed top of the standings but is now only 20 points clear of Robinson with three races remaining.
Aicher moved up to third, but with 96 points to make up on the Italian and another super-G scheduled for Sunday.
The race was halted briefly after Austrian Ricarda Haaser suffered a nasty crash and was taken off the slope on a stretcher.
American Lindsey Vonn, absent and out of action for the long-term after breaking her leg in an Olympic downhill crash, dropped to fourth in the standings.
