Martin rescued Vale with a fine save from Jevons in a one-on-one shortly afterwards as the rampant visitors continued to dominate.
But Vale had worked their way back into the contest before a stroke of good fortune led to Morecambe doubling their lead six minutes before half-time. An intended pass by Jevons was inadvertently deflected by Vale midfielder Doug Loft into the path of Mullin and he made no mistake from 12 yards.
Vale boss Micky Adams rung the changes in the second-half when his misfiring team at least had more of a go.
Barry Roche was forced to make one fine save from Marc Richards in the 53rd minute, but Morecambe defended in some comfort after that as the home side ran out of ideas.