But any neutrals in the ground would have found it hard to believe that it was Hereford who were the lower-graded outfit, as they completely outplayed their visitors.
Luke Webb cracked home the first five minutes before the interval and there were two from Rob Purdie at the start of the second period, before Andy Ferrell's spectacular strike rounded it off seven minutes from the end.
Nothing went right for the visitors with their woes starting in the warm-up when Akpo Sodje was injured and had to be replaced by Stefan Moore in the starting line-up.
Hereford had much the better of the first-half action and the only surprise was that it took until the 41st minute to take the lead.
As early as the fourth minute, Andy Williams had a shot blocked after a good build-up involving Tamika Mkandawire and Purdie.
Five minutes later, Tim Sills flicked a header just wide after a fine run and cross by Williams.
Alan Connell and Purdie worked a good opening for Sills who curled his shot inches wide on 16 minutes and Williams curled an effort just over after good work by Ferrell two minutes later.
Although Vale forced three first-half corners to Hereford's none, the visitors' attack posed few problems as the Bulls' defence excelled.
There were long-range efforts from Clayton Fortune, whose 30-yarder was well held by Wayne Brown underneath his crossbar, and Leon Constantine, who drove over from 20 yards. But these apart, a couple of goalmouth scrambles were the only moments of concern for the home side.
Connell's long-range shot drifted wide on 39 minutes, but the breakthrough came just a minute later.
Alex Jeannin's throw was flicked on by Connell to Webb who fired into the roof of the net past goalkeeper Mark Goodlad from 20 yards.
It was the youngster's second goal in the competition after also scoring in the first-round replay against Shrewsbury.
After Vale forced a corner within ten seconds of the re-start, it was Hereford who were swiftly back on the rampage.
Sills raced through on to a long headed pass from Mkandawire and was brought down by keeper Goodlad as he sped into the area.
Purdie stepped up to score from the spot, his eighth successful conversion from eight attempts this season.
Two minutes later, he added his first of the campaign from open play, but this owed something to the inadequacies of the Vale defence.
Purdie raced away on to a Connell pass and drove in a low cross which dribbled into the corner of the net as George Abbey produced football's equivalent of a golfing air-shot.
Webb forced Goodlad into a fine save minutes later as Hereford continued to press forward and it was the Bulls who continued to have much the better of play, although Constantine might have done better with a header from Moore's cross which went wide.
Hereford continued to force the pace and were rewarded with their fourth and best goal of the game seven minutes from time.
The outstanding Purdie won the ball in midfield and slipped the ball to Sills who made ground on the right before crossing. The ball reached Ferrell arriving at the edge of the area and the Tynesider's volley screamed past Goodlad into the top corner of the net.