Marco Rossi’s side took the lead just two minutes into proceedings, when Callum Styles passed the ball behind Dara O’Shea for Barnabás Varga to clinically finish despite being pushed by the centre-back.
Ireland showed intent of their own with shots from Finn Azaz and Sammie Szmodics that ultimately went wide.
However, having already escaped further punishment when Varga headed wide after losing Nathan Collins, Ireland’s deficit was doubled on the quarter-hour mark with Roland Sallai rising superbly to guide Dominik Szoboszlai’s corner inside the far post.
Jake O’Brien epitomised Ireland’s frustrations in two encounters with Sallai, but Hungary weren’t taking anything for granted as Styles and Dénes Dibusz bravely put their bodies on the line to ensure Josh Cullen and Azaz couldn’t provide a route back into the game.
Willi Orbán then stopped a Ryan Manning cross and shot, before Matt Doherty and Evan Ferguson sent an effort apiece wide. There was an eye-catching save at either end before the break, as Caoimhín Kelleher got down to deny Sallai and Dibusz palmed away a venomous Ferguson strike.
Ireland struck back four minutes after the restart, though, as Dibusz unconvincingly dealt with Manning’s free-kick, allowing the ball to be kept alive long enough for Ferguson to turn home.
A previously despondent Aviva Stadium was now filled with belief, and that grew four minutes later when Sallai was sent off for retaliating to not being given a free-kick by charging into O’Shea.
Bendegúz Bolla had four attempts as the visitors tried to regain control, while Manning went close with a header between those. The Irish pressure was relentless, but Collins missed the target twice and Dibusz spectacularly saved Azaz’s header.
The Hungarian goalkeeper then stopped a Chiedozie Ogbene strike and a Manning free-kick. However, refusing to be denied, Ireland finally got their hard-earned equaliser in the 93rd minute as Adam Isah rose to head home Manning’s cross.
Things could have got even better with O’Shea heading off target, but the point provides a boost to Ireland’s hopes of reaching their first World Cup finals since 2002.
It was also a blow for Hungary, who have won one of their last seven matches and last played in the finals in 1986.
Flashscore Man of the Match: Ryan Manning (Republic of Ireland)