Leo Bertos and Celtic's Chris Killen both hit the woodwork while a Fallon header was brilliantly saved by goalkeeper Sayed Jafaar.
Fallon did strike just before the break but the visitors were handed a route back into the tie when Tony Lochhead fouled Abdulla Omar in the box although Paston stopped Adnan's weak effort.
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.
"This group of players has given everything to achieve this dream, everything over the last four years," said New Zealand coach Ricki Herbert, who was a member of the defensive line that played in Spain.
"It's incredible. We're back. We're there."
New Zealand skipper Ryan Nelsen, who plays for Blackburn, paid tribute to the 35,100 fans in Wellington - a record for a football match in the country.
"The crowd was incredible and I don't know if we could have won it without them," he said.
"They were our 12th man today and they got us home. I've played in some incredible atmospheres but this is right up there."
Bahrain also came close to securing a place at the last World Cup but lost out to Trinidad and Tobago at the same stage.
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