Hungary appeared to be heading for victory when Balazs Dzsudzsak's vicious inswinging corner was nodded in by substitute Tamas Priskin in the 75th minute.
The visitor's response was emphatic with substitute Niall McGinn tapping the ball into the empty net six minutes later after fine work by Lafferty.
The 26-year-old Lafferty then grabbed the winner when he was first to react to bundle in a loose ball after McGinn's dangerous cross.
"The result is fantastic. When we went a goal behind we had the strength and belief and could turn the game around," Northern Ireland coach Michael O'Neill told reporters.
"It is huge for us, we played well tonight. I think we deserved the win."
Attila Pinter, who marked his first competitive match in charge of Hungary, said: "It's a great disappointment, but we made silly mistakes after we had the lead.
"Unfortunately we were a man behind for the last 10 minutes after our defender Zoltan Liptak was injured but he had to stay on as we already made three substitutions. It is a long campaign, but there are lots of adjustments to make."
(Editing by Martyn Herman)
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