Bank sped down the Rosa Khutor course in 1 minute, 54.32 seconds. Dominik Paris of Italy was second, 0.06 behind, and Miller was 0.17 behind.
Downhill gold medalist Matthias Mayer was fourth, 0.24 behind, and Ivica Kostelic of Croatia—who took silver in combined at the last two Olympics—was sixth, 0.79 behind.
World champion Ted Ligety was 11th, 1.46 behind, and French contender Alexis Pinturault was 12th, 1.80 behind.
Aksel Lund Svindal was among 16 racers who sat out.
Friday's winner will be determined by adding the times together from one downhill run and one slalom leg.