Kroell broke his drought with a run of 2 minutes, 31.28 seconds, a scant .14 seconds ahead of Cuche.
Switzerland's Carlo Janka came in third at 2:31.67. Bode Miller was the top U.S. finisher in eighth place. Austria's Michael Walchhofer finished 11th but held on to the lead in the downhill standings.
Conditions on the venerable and demanding Lauberhorn course were described as perfect, and a large number of Swiss fans lining the hill made for a festive atmosphere, especially with Cuche and Janka making the podium.
"This was an incredible first experience," said American rookie Wiley Maple. "There were thousands of fans here and so much energy."
Police: Sword-wielding man demanded free tacos
Campus cop fatally shoots Texas student during traffic stop