The two sides will join USA, Thailand, Turkey and hosts China in Ningbo from June 27 to July 1 for the Finals.
Brazil needed just three sets to deal China their first loss of the tournament while Cuba beat NORCECA rivals Puerto Rico by the same margin.
Meanwhile, world No.1 USA beat Thailand, Germany saw off Turkey, Serbia defeated Argentina, Japan won their all-Asian clash against Korea, the Dominican Republic took the honours against Chinese Taipei and Italy edged Poland.