We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional Renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [( p + q)/ Λ] − δ in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, Λ is a renormalization mass, and δ is a suitable non-integer: the analog of ε in dimensional schemes. All Dirac algebra and integrations are four-dimensional, and renormalization is achieved by subtracting poles in δ, followed by setting δ → 0. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is by-passed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.