Despite dominating the game, the Australian international came off the bench in the second half to claim an unlikely win for the SkyBet Championship strugglers.
And while both sides had penalty decisions waved away by Tyne & Wear official Scott Duncan, the Brewers failed to create a single effort in the opening 45 minutes.
The second-half fared little better, despite the introduction of forwards Elias Kachunga and Nahki Wells with Town's misery compounded by Dean Whitehead's dismissal for a second bookable offence in the 88th minute before Irvine sealed all three points in stoppage-time.
The defeat leaves Town in third position but crucially now nine and ten points behind Brighton & Hove Albion and Newcastle United respectively.
The fortnight's break for international football felt like an eternity, especially after signing off with the heavy Ashton Gate defeat as Town started the game patiently playing the ball around.
Burton's tactics were blatantly obvious from the offset, playing a narrow 3-5-2 formation with plenty of men behind the ball in order to keep the game tight and frustrate a free-flowing Huddersfield Town.
However, the Brewers were nearly undone within the opening minutes, Aaron Mooy, with far too much space, spraying a wonderful cross-field pass to Smith – the full-back's initial effort well saved by Jon McLaughlin before being subsequently ruled offside.
After that Town dominated, having 75% of the first-half possession without truly troubling McLaughlin in the Burton goal – although they should have had a penalty in the 23rd minute when Smith went down in the box under pressure from Tom Flanagan.
It wasn't given though – neither was the one minutes later at the other end when the aforementioned Flanagan went down in the box after a collision with Christopher Schindler.
Referee Scott Duncan had appeared to even up his ineptitude by denying both sides what looked clear penalties, and his generally poor performance further hindered the opening 45 minutes as the game became a scrappy and niggly affair.
It suited Burton Albion's game plan, with the second period following the similar pattern to the first as Smith once again had the best of the early chances, firing a speculative shot over the bar from 20 yards out.
Sensing the necessity to mix things up, Wagner brought on Kachunga and Wells for Lolley and Payne with Nigel Clough quickly responding with the introduction of Burton's top goalscorer Jackson Irvine.
But despite the changes, Town could still not find a way through the stubborn Brewers backline with the visitors arguably having the best chance of the half with their only effort on goal.
As the clock dwindled down, Northern Irish full-back Flanagan found himself free in the box with Danny Ward, a spectator for the majority of the game, making a fine save to keep the scores level.
Town continued their quest for an elusive winner which they nearly found when Rajiv van La Parra's cross found Hefele's head – only for it to be cleared off the line by John Brayford.
The resultant melee then saw an altercation in the box between captain Whitehead and Flanagan for an off-the-ball incident which resulted in the Town midfielder sent off for a second bookable offence.
Undeterred, Town continued to push forward during the six minutes of stoppage time, but were dealt another blow as Irvine found the back of the net with a breakaway goal to seal an unexpected win for the visitors.