Resolution enhancements are often desired in imaging applications where high-resolution sensor arrays are difficult to obtain. Many computational imaging methods have been proposed to encode high-resolution scene information on low-resolution sensors by cleverly modulating light from the scene before it hits the sensor. These methods often employ movement of some portion of the imaging apparatus, only to acquire images up to the resolution of a modulating element, or require extensive postprocessing to recover the high-resolution image. In this paper, a technique is presented for resolving beyond the resolutions of both apointwise-modulating mask element and a sensor array through the introduction of a controlled blur into the optical pathway. This proposed “hardware” superresolution method can be applied without machine learning and is shown to outperform standard software-only methods. The analysis contains an intuitive and exact expression for the overall superresolvability of the system, and arguments are presented to explain how the combination of random coding and blurring makes the superresolution problem well-posed. Experimental results demonstrate that resolution enhancements of approximately 4× and higher are possible in practice using standard optical components, without mechanical motion of the imaging apparatus, and without any a priori assumptions on scene structure.