Iceland equalised midway through the first half when Jon Guoni Fjoluson headed home a corner from close range.
Peru took the lead again 12 minutes into the second half when Raul Ruidiaz slotted home from a tight angle before Jefferson Farfan got the third when his shot from 12 yards out took a deflection that wrongfooted the goalkeeper and trundled home.
The victory came four days after Peru beat Croatia 2-0 in Miami.
Peru are heading to their first World Cup in 36 years this summer and will face Denmark, France and Australia in Group C.
Iceland, who are preparing for their first appearance at the finals, begin their Group D campaign against Argentina on June 16 before playing Nigeria and Croatia.
(Repofrting by Andrew Downie; Editing by Peter Rutherford)
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