Victory on the 10th anniversary of their famous win over England would have secured Michael O'Neill's men a place in France next summer, but the night looked set to end in acrimony as Michael McGovern's goalkeeping error gifted Richard Guzmics the opener in the 74th minute.
Chris Baird was sent off with eight minutes left, having committed a pair of fouls within seconds, but Lafferty's seventh strike of the campaign - a close-range blast following up Niall McGinn's effort - ensured a point.
With Romania drawing against Greece, O'Neill's men remain top of Group F - though Lafferty will miss the potentially decisive clash with the Greeks next month having picked up a second booking.
It was a frenetic, febrile finish in Belfast but once again showed Northern Ireland's desire to reach a first major tournament in 30 years is alive and kicking.
Lafferty celebrated his close-range effort with gusto, charging down the flank and leaping in joy, but even he cannot have been as pleased as McGovern, whose handling error looked to have settled matters.
Having been retained ahead of long-standing number one Roy Carroll, it was a dreadful moment for the Hamilton stopper.
The game started at a frenetic pace, with Northern Ireland captain Steven Davis tearing into a thunderous tackle just a minute into proceedings and a scattering of rushed passes hurting the flow.
Hungarian dangerman Balazs Dzsudzsak took an early chance to run at the home defence but screwed wide as the green shirts sat off him.
It was his only threatening moment of the first half, a minor feather in the cap of Chris Brunt, who is still not a natural left-back.
Lafferty and Guzmics traded bookings, with the Northern Irishman also targeted by a handful of red shirts.
One free-kick earned Oliver Norwood the chance to put his laces behind a swirling 30-yarder, but Gabor Kiraly managed a tumbling low save.
Conor McLaughlin joined Lafferty in earning a one-game ban when he was booked for a push on Kalmar, whose free-kick was creeping under the bar until McGovern pushed it over.
The 31-year-old's next involvement ended in tears as he came to claim a regulation catch from Dzsudzsak's hanging free-kick.
Inexplicably he let the ball slide through his gloves, leaving a disbelieving Guzmics a one-yard finish.
Worse was to come when Baird hacked down Kalmar, having committed an off-the-ball foul seconds earlier.
He was booked for both and, after a lengthy row with the referee, dismissed.
The five minutes of injury-time that resulted from that fracas ended up costing Hungary victory.
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With just about their final chance of the evening, a hard-won corner on the right, Davis heaved one last delivery into the box.
The ball fell to McGinn, whose snap-shot was well stopped by Kiraly.
But that man Lafferty, unable to get a game at Norwich, unable to stop scoring international goals, belted home first time to grab a critical point.
MICHAEL McGOVERN: Retained ahead of Roy Carroll and almost cost his side dearly with a dreadful handling error that led to the goal. Four out of 10.
CONOR McLAUGHLIN: Started with his usual solidity on the right and tested the water going forward when he settled into the game. 6
CHRIS BRUNT: Charged with marking dangerman Dzsudzsak, the West Brom man shaped up well at left-back and attacked the space in front when it opened up. 6
JONNY EVANS: Not a night for elegant sorties up the pitch, Evans kept it simple and did the chasing job when balls went over the top. 6
GARETH McAULEY: Another controlled performance from the veteran centre-half. Kept touch-tight to Adam Szalai and won his headers. 7
CHRIS BAIRD: Very impressive anchor work at the base of midfield until he was sent off in a frenetic conclusion for two fouls in a matter of seconds. 6
OLIVER NORWOOD: Drew a tumbling save with a swirling 30-yard free-kick and his set-piece delivery kept Hungary on their toes throughout. 7
STEVEN DAVIS: Bags of energy from the skipper, as is standard. Covered acres of ground and delivered the corner that led to the equaliser. 7
CORRY EVANS: Recalled to add discipline on the right flank and turned in a low-key display before making way for McGinn. 5
STUART DALLAS: The liveliest attacking presence on the park in the first half, running with and without the ball to pose questions. Faded before being replaced. 7
KYLE LAFFERTY: A quiet night for Northern Ireland's leading light until the depths of injury-time where his poacher's instinct took over and he smashed his seventh of the campaign from point-blank range. 7
NIALL McGINN (for C Evans, 56mins): Appears to be a more effective substitute than a starter. His smart shot led to Lafferty's equalising chance. 7
JOSH MAGENNIS (for Norwood, 75): Added as a second striker as Northern Ireland hunted an equaliser and made his presence felt. 6
SHANE FERGUSON (for Dallas, 83): On the pitch at the end but scarcely involved. 5
The squad is on the brink of its first ever European Championship finals and a Windsor Park win over Hungary would seal the deal for the Group F table-toppers.
Long-suffering Northern Ireland fans celebrated over the weekend after Friday's 3-1 win in the Faroe Islands - and hopes are high that the team can seal the deal tonight.
Former players, commentators, fans and politicians, including First Minister Peter Robinson, have all lined up to cheer on Michael O'Neill's squad.
Among the 'super-fans' at Windsor Park will be 95-year-old Canon Edgar Turner, who is just back from the Faroe Islands. He said it was "tiring" but worth every minute.
"I thoroughly enjoyed the experience and I'm absolutely delighted to be going to Windsor Park," he said.
"It is history, this Hungary decider. I can't prove I'm the oldest supporter. I know a number of elderly people who go to the home matches and some of them used to claim they were the oldest."
Gary McAllister from the Northern Ireland Supporters Club said the mood of expectation was high among fans.
"It would be a tremendous boost for the fans, a huge boost for Northern Ireland football and a huge boost for the country as a whole if they were to win," he said. "What they have achieved so far is tremendous and they are already heroes but there is an opportunity to become legends as in 1958, 1982 and 1986."
Among those making score predictions at the South Belfast Northern Ireland Supporters Club yesterday were Stephen Wilson (41), from Carrickfergus, and Ian Moore (66), from Belfast.
"This will be the biggest thing since Healy's goal against England," said Stephen. "It's been downhill since then but now we are on the up. I'm predicting a nil-nil draw but the result will be better against Greece or Finland."
Ian said: "I would like to hope for a one-nil result but we need a draw to get through to the next round. Michael O'Neill has done an excellent job."
Joining them was Jeff Handley (54), from Bolton, who became a fan when Northern Ireland beat England 10 years ago.
"I met great friends then and I have come back here three or four times," he said. "Northern Ireland is not a big place but they have passion about football."
Tommy Boyd (57), from Belfast, who manages the club, added: "This place will be packed and we will be expecting some of the away supporters. It will be the biggest celebration since we beat England."
It's a big night too for the football pundits. Gerry Armstrong, the celebrated former Northern Ireland international footballer, hopes the team will "keep their concentration" amid the expectation.
"I would take a score of one-nil," he said. "We beat Israel one-nil to qualify for the World Cup in 1982. We are making history and all credit to them."
Sports commentator Jackie Fullerton said: "I will be at the game as a fan, remembering the glory days of qualifying for the 1982 and 1986 World Cup. It has been a long time coming but I think Michael O'Neill deserves a lot of credit."
First Minister Peter Robinson said tonight's game was "a chance for everyone to get behind the team".
"Northern Ireland is truly within touching distance of qualifying for our first tournament in 30 years," he said. "Many fans have already made their arrangements for France next year and the scene is set for yet another memorable night at Windsor Park. I send my best wishes to the team and will be cheering them all the way."
Ulster Unionist Party leader Mike Nesbitt said the game was a opportunity for some "good news".
"If they make it to France, it will give the whole country a massive lift in terms of social cohesion," he said.
"When we beat Spain at their own World Cup in Valencia we had no idea how it had brought everyone together in common cause. The players' only regret was that they could not click their fingers and time travel back to Northern Ireland to celebrate with the people."
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