Left back McHugh guided Gary Jones' corner past goalkeeper Chris Neal, who had been in solid form, to secure a 1-0 victory in Tuesday night's League One clash at Valley Parade.
Bradford needed a confidence boost but they found former Shrewsbury 'keeper Neal in defiant mood as he pulled off excellent saves from James Hanson and Adam Reach.
Rory McArdle rescued City by heading out from under his own crossbar after Chris Lines spotted home 'keeper Jon McLaughlin off his line and tried a speculative lob from the right.
However, Vale's best chance fell to skipper Doug Loft, who could not beat McLaughlin from a few yards out.
Winger Reach, on loan from Middlesbrough, and captain Jones were Bradford's most potent weapons but Vale's mean defence restricted opportunities, with Jack Grimmer and Joe Davis keeping a close watch.
Bradford's luck was out when Reach saw his powerful angled shot thud back off the near post in the 76th minute but the Bantams' intense pressure finally told late on.