Manchester City striker Santa Cruz scored from the penalty spot four minutes from time.
Marcelo Estigarribia and Eduardo Ledesma both went close to scoring for Paraguay but were denided by the woodwork.
North Korea's Ri Jung-il almost put through his own net as Paraguay dominated the second half.
Paraguay were awarded a penalty on 86 minutes when Nam Song-chol handled the ball inside the box and Santa Cruz converted from the spot.
Both teams are holding training camps in the region, Paraguay in Evains-Les-Bains on the French side of Lake Geneva and North Korea in the Alpine village of Ayent as they continue their plans for next month's finals.
Paraguay are in Group F alonside Italy, New Zealand and Slovakia, while North Korea, who are in the finals for the first time since 1966, are in Group G with Brazil Ivory Coast and Portugal.