TROY PARROTT scored a stoppage-time winner as Ireland claimed their first win in eight months.
Parrott ran from his own box following a corner for Hungary as he collected Sammie Szmodics header which was inadvertently helped on by Callum Styles.
Szmodics kept pace in support but was in danger of being called inside so Parrot went it alone.
Substitute keeper Dénes Dibusz got a touch to his shot but could not keep it out.
Earlier Adam Idah and Adam Lang had traded goals within five minutes of each other in the first half.
It was a remarkable contribution from Parrott who, on Sunday, had scored a hat-trick which proved in vain as Excelsior lost their relegation play-off 6-5 on aggregate to NAC Breda.
There may be plenty of room for improvement in many aspects of Ireland’s play but to record a win is no mean feat and it was achieved by scoring with their only two efforts on target.
In their previous 11 matches, the only team Ireland had beaten was Gibraltar, twice. This was their most notable scalp since beating Scotland two years ago.
Whether it is enough to nudge John O’Shea closer to the job on a permanent basis remains to be seen but, for now, he will savour the victory, as unlikely as it was.
O’Shea had spoken before about the importance of tactical flexibility.
And, here, he put out a team which switched from a back five when without the ball to a four when they were in possession
That allowed Matt Doherty and Robbie Brady to join in as an extra attacker and, although it did not always function as the manager would have liked, it did contribute to the opening goal.
Doherty advanced on the right and looked as though he would swing a deep cross into the box. Instead he prodded the ball forward for Will Smallbone to run in behind.
The midfielder – who has just helped Southampton to win promotion – slung in a good cross with Idah’s movement deceiving the centre-halves before he powered a header home.
The opening goal was, it had to be said, against the run of play.
O’Shea had, for the most part, opted for a tried-and-trusted line-up with the uncapped Jake O’Brien, Tom Cannon and late addition Bosun Lawal left on the bench.
His one concession to experimentation was to hand Finn Azaz – who had made his debut as a substitute against Switzerland– his first start.
It soon had the look of a night for which a lot of graft would be required with Ireland reasonably content to surrender possession and territory and defend in banks of five and four.
There was an early chance for the visitors when the ball sailed over the heads of both Barnabás Varga and Shane Dufy.
The pair raced to retrieve it and it was prodded towards Loic Nego but he could not profit in front of goal, firing wide.
Appeals for a free-kick for a challenge by András Schafer on Josh Cullen were then waved away as Hungary broke with purpose.
Milos Kerkez was played through on the left side of the box but Caoimhín Kelleher was equal to his shot.
Ireland took the lead in the 35th minute. Idah went 13 games without a goal at the start of his international career.
But he has now scored four times in his last 10, with six of those appearances coming as substitute, with his confidence levels enhanced by a profitable loan spell at Celtic.
However, Ireland were pegged back within five minutes as anything that could go wrong did go wrong.
The home side retreated into their box in the expectation of an immediate, long delivery from a free-kick.
Instead, Adam Nagy played it short to Dominik Szoboszlai who advanced unhindered before Azaz moved to press.
He succeeded only in helping the Liverpool man’s pass on with a deflection. Will Orban won the flick-on to help it on to Lang.
Replays suggested that he was offside but, in the absence of VAR, there was no chance of it being disallowed once the assistant referee’s flag had not been raised.
Ireland could have regained their advantage before the break with Idah getting on the end of a Brady free-kick but it would have been more than they deserved.
There were changes made at the break with O’Brien coming on for his debut, with Liam Scales also introduced, with Troy Parrott, Callum O’Dowda, Michael Obafemi and Jason Knight subsequently brought on.
The Youghal man stands out because of his physique but there is more to him than that as a first-time pass to Parrott, who had dropped deep, showed.
Parrott was welcomed to proceedings by having the ball smashed at him by Szoboszlai.
The rancour continued and eventually led to a booking for the Hungary captain and his Ireland counterpart Séamus Coleman which presumably will recede by the time they return to being neighbours on Merseyside.
It was a brief moment of intensity with the rest of the second half resembling what this was, a friendly between one side going to a major tournament and another who was not but bidding to provide some evidence that it could do so in the future.
Sadly, Ireland’s goalscoring opportunities were few and far between, although they did also limit their opponents to just a few half-chances.
One of those was a shot from 20 yards from Roland Sallai.
Given how many goals were conceded from outside the box during Stephen Kenny’s reign, with many pointing the finger of blame at Gavin Bazunu, it was a relief to see Kelleher – at full stretch – pushing it away.
Coleman squandered a late chance and it looked set to be honours even before Parrott took matters into his own hands.