Hungary looked to have breathed life into their qualifying campaign with a late Richard Guzmics goal after a goalkeeping howler by Ireland's Michael McGovern before Lafferty struck.
The Irish striker rifled the ball home in the third minute of added time to salvage a point after Hungary stopper Gabor Kiraly spilled Niall McGinn's shot following a corner.
The draw puts Northern Ireland on 17 points ahead of Romania, who have 16 after a 0-0 draw with bottom side Greece on Monday, and Hungary on 13 with two games left to play.
"This squad is willing to fight to the end," Lafferty, who also popped up to score a late winner in the first group game between the two sides in Budapest, said in a post-match TV interview. "This side doesn't know when to stop working.
"We have two games left and we need one more push," he said, adding that he regretted the 10th-minute yellow card that will see him suspended for the next game at home to Greece.
Also out of that match is midfielder Chris Baird, who was dismissed seven minutes from time for a second bookable offence as his side struggled desperately for an equaliser.
The Irish were hoping to secure qualification for the European championship for the first time with a win at Windsor Park but failed to create chances despite plenty of possession.
After a period of second-half Hungarian pressure, McGovern failed to hold a harmless-looking free kick and Guzmics was on hand to bundle the ball home in the 74th minute.
But just when it looked like the visitors would take home all three points Lafferty struck to keep Northern Ireland in pole position in the section.
Northern Ireland face Greece and Finland in their last two games while Hungary take on the Faroe Islands and the Greeks.
A win in one of their final two fixtures would see the Irish reach their first finals since the 1986 World Cup in Mexico.
(Reporting by Philip O'Connor; Editing by Ken Ferris)
