After the Warriors benched center Andrew Bogut to return to their run-and-gun style in a 21-point Game Four victory, Cleveland responded by limiting starting center Timofey Mozgov to just nine minutes on Sunday.
The move kept Cleveland close deep into the fourth quarter until Andre Iguodala scored five straight points to put Golden State ahead 91-84 with less than four minutes remaining.
Curry, who scored 17 points in the fourth, added two late three-pointers and free throws to help seal the win.
Iguodala finished with 14 points, eight rebounds and seven assists. James tallied 14 rebounds and 11 assists for his second triple-double of the series.