Curry hit four 3-point shots for the Blue Devils (12-0), who got 22 points and 13 rebounds from Mason Plumlee, and 10 points and 11 rebounds from Ryan Kelly.
Duke shot 49 percent from the field and was 7-of-14 from 3-point range.
Kevin Foster led Santa Clara (11-3) with 29 points. Evan Roquemore scored 17 and led the Broncos with six rebounds.
Duke held a slim 38-36 lead at halftime and fell behind 45-41 early in the second half. The Blue Devils then went off on a 13-1 run that included two 3-pointers from Curry to take control.