Edison Flores doubled their lead three minutes into the second period when he poked the ball home from close range after a quick counterattack.
Peru had Yoshimar Yotun sent off after 74 minutes but the Croatians found goalkeeper Carlos Cacida in fine form.
Peru, who will compete in the World Cup finals for the first time since 1982 this summer, kick off their campaign on June 16 against Denmark and then face France on June 21 and Australia on June 26.
Croatia play Nigeria in their opening match on June 16, before taking on Argentina five days later and then playing Iceland on June 26.
(Reporting by Andrew Downie; Editing by Peter Rutherford)
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