Vale celebrated coming out of administration with a thumping victory over Bristol Rovers on Tuesday and Micky Adams' side made it two wins in five days to consolidate their hold on second place in League Two, closing the gap on leaders Gillingham to just two points.
Ben Williamson put the Valiants ahead after 17 minutes of Saturday's League Two clash at the EBB Stadium following some neat interplay with Tom Pope on the edge of the box, but the Shots were level just after the half-hour mark - Dani Lopez nodding home from close range.
Pope, League Two's top marksman, could have given the visitors the lead five minutes before the break from a Burge corner but Jamie Young got down well to save his goalbound header.
Vale did not have to wait long to move in front, however, Burge slotting home after Pope's 47th-minute header was saved.
Danny Rose's curling free-kick almost levelled it for the Shots but Myrie-Williams made the points safe when he tucked away from the spot, after he had himself been fouled by Troy Brown with 16 minutes remaining.