Goalkeeper Mark Paston saved a second-half penalty to preserve New Zealand's lead in the second leg of the Asia/Oceania World Cup qualifier after the first leg in Manama had ended 0-0 last month.
New Zealand, champions of the Oceania zone, had their only previous World Cup appearance in Spain in 1982.
"I've been very honest about the quality of this team," New Zealand coach Ricki Herbert told reporters. "They've all worked hard. We all backed the system and we truly believed it was good enough to win and they have gone and done it."
Fallon, whose father Kevin was assistant manager of the 1982 side, sealed their ticket to next year's finals in South Africa when he powered home Leo Bertos's corner in the final minute of the first half at a sold-out Westpac Stadium.
"I always fancy myself when the boys put the balls in and I have been scoring lately at my club so I just visualised it today and I knew I could do it," Fallon said.
"That is the belief that Ricki has been going on about. Everyone had that belief. Leo put in a great cross and I put it away."
However, Sayed Adnan's weak effort was easily saved by Paston to the delight of most in the 35,194 crowd.
"I actually guessed," Paston said of his save. "They were trying to tell me what way he goes, but the message didn't get on and I just guessed.
"It was great to save a penalty, but the whole second half the boys in front of me were incredible and it comes down to that. It was amazing what they did for me."
New Zealand's Shane Smeltz had an opportunity to kill the game off in the 70th minute when he was put through by Bertos, but his deft flick went just wide.
