Nano-oils comprising stable and dilute dispersions of synthesized Graphene (Gr) nanoflakes and carbon nanotubes (CNT) have been experimentally observed for the first time to exhibit augmented dielectric breakdown strengths compared to the base transformer oils. Variant nano-oils comprising different Gr and CNT samples suspended in two different grades of transformer oils have yielded consistent and high degrees of enhancement in the breakdown strength. The apparent counter-intuitive phenomenon of enhancing insulating caliber of fluids utilizing nanostructures of high electronic conductance has been shown to be physically consistent thorough theoretical analysis. The crux mechanism has been pin pointed as efficient charge scavenging leading to hampered streamer growth and development, thereby delaying probability of complete ionization. The mathematical analysis presented provides a comprehensive picture of the mechanisms and physics of the electrohydrodynamics involved in the phenomena of enhanced breakdown strengths. Furthermore, the analysis is able to physically explain the various breakdown characteristics observed as functions of system parameters, viz. nanostructure type, size distribution, relative permittivity, base fluid dielectric properties, nanomaterial concentration and nano-oil temperature. The mathematical analyses have been extended to propose a physically and dimensionally consistent analytical model to predict the enhanced breakdown strengths of such nano-oils from involved constituent material properties and characteristics. The model has been observed to accurately predict the augmented insulating property, thereby rendering it as an extremely useful tool for efficient design and prediction of breakdown characteristics of nanostructure infused insulating fluids. The present study, involving experimental investigations backed by theoretical analyses and models for an important dielectric phenomenon such as electrical breakdown can find utility in design of safer and more efficient high operating voltage electrical drives, transformers and machines. © 1994-2012 IEEE.