Santa Cruz struck his spot kick high to the left of goalkeeper Ri Myong Guk after substitute Nam Song Chol was harshly adjudged to have handled the ball.
Paraguay hit a post twice in a seven-minute spell midway through the second half.
Choe Kum Chol had North Korea's best chance in the 35th but lifted his shot over the bar.
Paraguay plays Ireland in Dublin on May 25, the same day North Korea meets fellow World Cup qualifier Greece in Austria.
At the World Cup, Paraguay faces plays defending champion Italy, Slovakia and New Zealand in Group F.
North Korea is grouped with Brazil, Ivory Coast and Portugal in Group G, what many think is the most difficult group.