Gary Roberts handed League Two Vale the lead midway through the first half but the Terriers had turned matters around within 14 minutes thanks to a brace from the incoming Lee Novak.
Jack Hunt then added a blistering third from distance after the break before Terriers midfielder Gary Roberts matched his Vale namesake by getting his name on the scoresheet - taking Huddersfield's goal tally in the League Cup to 200. Doug Loft grabbed a late consolation for Vale from the spot.
Brothers Jamie and John McCombe came up against each other for the first time in their professional careers. And it was Vale's John McCombe who had reason to celebrate first as team-mate Roberts slotted home from close range.
But the home side's lead lasted all of five minutes as Novak replied from six yards out at the other end. And the Terriers marksman, one of six changes by Lee Clark, handed the League One side the advantage at the break as he received a pass from Hunt before lashing into the top corner.
Hunt himself got in on the act just in stunning style before the hour mark before Town midfielder Roberts put the tie beyond reach, receiving a free-kick from Gary Naysmith before converting from 25 yards. But there was still time for Loft to slot home a spot-kick after Naysmith had fouled Anthony Griffith in the penalty area.