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We report a rapid solution-phase strategy to synthesize alloyed PtNi nanoparticles which demonstrate outstanding functionality for the oxygen reduction reaction (ORR). This one-pot co-reduction colloidal synthesis results in a monodisperse population of single-crystal nanoparticles of rhombic dodecahedral morphology, with Pt enriched edges and compositions close to Pt1Ni2. We use nanoscale 3D compositional analysis to reveal for the first time that oleylamine (OAm)-aging of the rhombic dodecahedral Pt1Ni2 particles results in Ni leaching from surface facets, producing aged particles with concave faceting, an exceptionally high surface area and a composition of Pt2Ni1. We show that the modified atomic nanostructures catalytically outperform the original PtNi rhombic dodecahedral particles by more than 2-fold and also yield improved cycling durability. Their functionality for the ORR far exceeds commercially available Pt/C nanoparticle electrocatalysts, both in terms of mass-specific activities (up to a 25-fold increase) and intrinsic area-specific activities (up to a 27-fold increase).