Second in the first stage run on Saturday, Bauhaus (28) beat Frenchman Arnaud Démare (Groupama) and his compatriot Nikias Arndt (DSM).
Like the day before, a fall occurred at the end of the race.
900m from the finish, the peloton got caught in a tight bend, leaving only about ten riders the chance to battle it out in the final pack.
From the start of this hilly stage, a breakaway of six, then eight riders formed.
They were taken back three kilometers from the finish under the impetus of the Ineos formation of Ecuadorian Richard Carapaz, second in the last Giro.
But after the fall in the last kilometer, it was finally Bahrain who pulled out of the game with Bauhaus, who had already won a stage last year in this event.
An 11.8 km time trial is on the menu for the sixth and penultimate stage on Thursday.
Higuita is only four seconds ahead in the general classification over the Spaniard Pello Bilbao (Bahrain) and six over the Belgian Quinten Hermans (Intermarché).
© 2022 AFP