Here, the reverse applied on an autumnal afternoon which proved to those in amber and black. It remains to be seen if it provides another significant moment to their season.
Victory in this huge relegation six-pointer was richly deserved by City, who ended a five-match losing sequence in excellent fashion.
It was an occasion when all the battles were won by those in Hull jerseys. They possessed more conviction, urgency and willingness to fight for each other than those in red, who produced a timid offering after the midweek highs against Derby.
Hull took the lead on 33 minutes with their first away goal in ten and a half hours from George Honeyman, who set up the killer second 15 minutes from time from Keane Lewis-Potter, comfortably the best player on the pitch.
While Hull produced a very presentable away-day performance, Barnsley were a sorry mess by the end - and was a tough watch for everyone and most certainly caretaker head coach Joe Laumann, whose own hopes of landing the full-time position suffered a hefty blow.
Team changes ahead of the kick-off generated considerable interest, with Jordan Williams, Liam Kitching and Devante Cole coming in for Callum Styles, Mads Andersen and Victor Adeboyejo, who started on the bench.
But the more head-turning change arrived upon inspection of the Hull teamsheet with Nathan Baxter handed his league debut for the club, with Matt Ingram dropping to the bench.
In the event, aside from turning away a piledriver from Callum Brittain, the Chelsea loanee had nothing substantive to do in a half which saw the Tigers gain control and deservedly lead.
The goal they had been threatening arrived on 33 minutes and Barnsley could have no complaints whatsoever after being punished for a passive, low-octane half.
After a bright enough opening few minutes, Barnsley retreated into their shells and Hull - with the game’s most inventive and watchable player on the pitch in Keane Lewis-Potter - grew into the game, started to take control of midfield and carve out opportunities.
Early half-chances from Richie Smallwood and Josh Magennis flew off target, while Jacob Greaves nodded wide before Barnsley’s first opportunity arrived on 27 minutes.
An excellently-delivered free kick on the left from Josh Benson found the head of the unmarked Cole, who headed off target.
At the other end, Honeyman - who had been cautioned for a foul on Cole which led to a free-kick - had a more telling effect.
Lewie Coyle threaded an incisive pass down the right channel to the hard-working Magennis, whose low centre was diverted towards goal by Jasper Moon, with Brad Collins making a key block.
Unfortunately, the loose ball found its way to Honeyman, who stroked the ball home.
Soon after, a header from ex-Reds forward Mallik Wilks drifted wide, with Barnsley requiring the sanctuary of half-time to regroup - with Laumann faced with a test to repair the damage in his interval team-talk.
A change saw Cole make way and midweek scorer Victor Adeboyejo come on to provide Barnsley with a physical presence.
But as far as Barnsley were concerned, things almost got distinctly worse.
A defensive mishap saw Lewis-Potter afforded a surfeit of space down the left from Di’Shon Bernard’s probing pass and he squared to Honeyman and after his attempted strike was blocked, the ball found its way to Greg Docherty, whose point-blank attempt was saved superbly by the ever-reliable Collins - with Magennis blasting the rebound off target.
The Pontefract Road end turned up the volume in an attempt to rouse the hosts from their slumber, while another change quickly arrived with Styles replacing Jordan Williams.
Styles soon announced himself with a low shot which was grasped by Baxter before a key last-ditch tackle from Greaves thwarted Iseka as Barnsley finally stirred into life.
Just like in the first period, it was Brittain who was afforded the hosts’ big second half after good work by Iseka, but his shot was straight down the throat of Baxter.
It proved a big moment with City promptly securing victory with a second not long after on the break from the excellent Lewis-Potter.
A third almost arrived when Lewis-Potter set up substitute Longman, who hit the post while Collins then denied Smallwood.
Barnsley: Collins; Moon, Helik, Kitching; Brittain; Gomes, Benson (Palmer 72), J Williams (Styles 57); Cole (Adeboyejo 45), Woodrow, Iseka. Substitutes unused: Walton, Andersen, Vita, Frieser.
Hull City: Baxter; Coyle (Emmanuel 37), Bernard, Greaves, Elder; Smallwood, Docherty; Wilks (Longman 67), Honeyman, Lewis-Potter; Magennis (T Smith 67). Substitutes unused: Ingram, Cannon, McLoughlin, M Smith.
Referee: S Martin (Staffs).
Attendance: 13,003 (1,553 Hull supporters).