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We propose a novel mechanism for significantly enhancing the amplitude of primordial electromagnetic fields during inflation. Similar to existing proposals, our idea is based on parametric resonance effects due to conformal-symmetry-breaking coupling of a gauge field and the inflaton. Our proposed scenario, however, significantly differs from previously studied models, and avoids their shortcomings. We, particularly, construct a viable system where the gauge field is exponentially amplified on super-horizon scales, therefore evading the no-go theorem formulated on the basis of widely encountered drastic back-reaction of the magnetic field energy on the inflationary background. We argue that in order for the resonant scenario to work with a bounded and positive-definite coupling function, a mass term for the gauge sector is required. We compute the spectrum of the produced magnetic fields and demonstrate the compatibility with current observational constraints. We demonstrate that while the magnetic fields do not noticeably back-react on the inflationary background, the non-zero mass term can contribute significantly to the total energy-momentum tensor. We point out the parameter space where the latter issue is absent.