The draw in drenched conditions means Ireland extended their unbeaten run to 14 games - 11 achieved without conceding a goal - and Giovanni Trapattoni's men head for their opening game against Croatia next weekend with a clean bill of health.
"We were a little bit lucky, because in the first half we could have gone 2-0 down but Shay Given was terrific," Ireland coach Giovanni Trapattoni told a news conference.
"Our opponents deserved to go ahead, and at the end we could have lost 3-0. Hungary are quite a strong team, with good youngsters, playing some nice football.
Ireland started with the first choice XI that Trapattoni hopes to field in their first Group C game in Poznan on Sunday although goalkeeper Shay Given, who has been troubled by a knee injury, was replaced at half-time by Keiren Westwood.
The match, which started 20 minutes late because of heavy rain and constant lightning in the capital, saw the visitors create the first chance when their captain Robbie Keane forced Hungary goalkeeper Adam Bogdan into action in the 14th.
However, the impressive young home side quickly began to dominate and a fit-again Given had to make a smart save from a deflected Balazs Dzsudzsak shot moments later and stopped the Dynamo Moscow midfielder again after 24 minutes.
Adam Szalai was next to have a go and failed to take full advantage when a Sean St Ledger slip left him one-on-one with Given, although the striker would have made amends just before the break but for a brilliant sliding tackle by Stephen Ward.
The pressure on Ireland continued in the second half at Ferenc Puskas Stadium and Szalai had two further chances from close range after 53 and 54 minutes, his first blocked by St Ledger and the second stopped by a fine save from Westwood.
Fellow Irish substitute Jonathan Walters offered some respite with a stinging effort from a tight angle on the hour which was parried by Bogdan but the big forward somehow missed the target with a free header 20 minutes later.
Hungary remained dangerous on the break and finally beat Westwood after 84 minutes but Stephen Hunt was on hand to wallop substitute Imre Szabics's effort off the line.
The home side, who missed out on a place in Poland and Ukraine but won as many qualifiers as Ireland including a victory over Sweden, showed their intent to go one better when the World Cup comes around having done everything but score.
"I knew it was not going to be an easy game, but I did not want to change our system for one match," said Trapattoni.
"Against opponents who play with one striker we have difficulties. We will talk the problems over.
"Croatia's style is a bit different, against them, maybe we need one more midfielder," he added.
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