Random jammers that overpower transmitted signals are a practical concern for many wireless communication protocols. As such, wireless receivers must be able to cope with standard channel noise and jamming (intentional or unintentional). To address this challenge, we propose a novel method to augment the resilience of the recent family of universal error-correcting GRAND algorithms. This method, called Erasure Decoding by Gaussian Elimination (EDGE), impacts the syndrome check block and is applicable to any variant of GRAND. We show that the proposed EDGE method naturally reverts to the original syndrome check function in the absence of erasures caused by jamming. We demonstrate this by implementing and evaluating GRAND-EDGE and ORBGRAND-EDGE. Simulation results, using a Random Linear Code (RLC) with a code rate of $105/128$, show that the EDGE variants lower both the Block Error Rate (BLER) and the computational complexity by up to five order of magnitude compared to the original GRAND and ORBGRAND algorithms. We further compare ORBGRAND-EDGE to Ordered Statistics Decoding (OSD), and demonstrate an improvement of up to three orders of magnitude in the BLER.