Second-half goals from Sandor Torghelle and Zoltan Gera were enough to give the visitors a victory they deserved.
Yet the province went into the match in confident mood after beating San Marino comfortably in a World Cup qualifier last month.
However, Hungary dominated for long spells and almost took the lead in the 15th minute when the hosts were caught cold.
Krisztian Vadocz hoisted the ball over the top and Torghelle was the first to react but he failed to test goalkeeper Maik Taylor, who was captaining the side, dragging his effort wide from a good position.
Kyle Lafferty was then booked by Austrian referee Robert Schoergenhofer in the 29th minute for a challenge on Vadocz as the ball got away from him.
The Hungarians were busy and Vadocz dusted himself down, striding forward two minutes later.
He tried his luck on goal but his effort went closer to the corner flag than the goal.
The visitors were growing in confidence and Gergely Rudolf burst to the byline in the 33rd minute.
Rudolf managed to evade Chris Baird's challenge and laid the ball back to Szabolcs Huszti.
He got a good first touch, only to send his shot wide of the post from just inside the box.
Sammy Clingan and Roland Guhasz both went off in the 41st minute to receive treatment after an aerial collision but re-appeared before half-time.
Worthington made two changes at the interval, bringing on goalkeeper Jonathan Tuffey for his debut in place of Taylor.
With Taylor taking a back seat, Norwich midfielder Clingan wore the armband - and a bandage to cover the wound on his head.
Northern Ireland almost took the lead in the 54th minute when Chris Brunt swung in a cross from the left.
Gillespie did well to win the header from Peter Halmosi and the ball spun into the path of Healy but the goalkeeper cleared the striker's effort with his legs.
A minute later Worthington handed Niall McGinn his debut with the winger replacing Michael Duff.
Hungary, however, took the lead in the 57th minute after a surging run from Huszti. He clipped the ball back from the byline and Torghelle made no mistake from close range.
Northern Ireland then appealed for a penalty on the hour when substitute Warren Feeney was grounded by Roland Guhasz but the referee allowed play to continue.
The home side pressed forward again and McGinn's effort came back off the top of the bar as Hungary found themselves on the back foot.
However, the visitors regrouped and went 2-0 ahead in the 71st minute with a goal out of nothing from Fulham's Gera.
The midfielder latched on to a clearance from goalkeeper Gabor Babos and with Jonny Evans backing off, he rifled a superb shot into the net from 25 yards.
Babos then did well to parry Healy's free-kick as the home side attempted to get back in the game.
It was just a brief rally, leaving Hungary to take the spoils in the driving wind and rain.