The visitors will travel to Poland & Ukraine buoyed by another clean sheet, but evidenced some of the wasteful finishing that has blighted them in recent games
An open game saw both sides create chances but, whilst some of the approach play was good, the finishing - most notably from Hungary's Adam Szalai and Ireland's Jon Walters - left much to be desired.
The Magyars, ranked 35th in the Fifa world rankings and with only one loss in their last nine matches, named the talented Dinamo Moscow winger Balazs Dzsudzsak in midfield. However, they were without Tamas Priskin, who had scored three goals in his last three international matches, and chose Mainz striker Adam Szalai his replacement.
Giovanni Trapattoni named his strongest possible starting line-up featuring the 11 who, injury-permitting, will start Ireland's opening match of Euro 2012 against Croatia in Poznan.
That meant a return in goal for Aston Villa's Shay Given and at right-back for Sunderland defender John O'Shea, the pair having been struggling with knee and ankle injuries respectively. Elsewhere, Wolves striker Kevin Doyle started up-front alongside Robbie Keane, despite Shane Long's winning goal against Bosnia-Herzegovina nine days previous.
With rain teeming down in Budapest the kick-off was delayed for 15 minutes, but when play did eventually get underway it was Ireland who had the first effort on goal and from an unlikely source.
A free-kick on the right was worked short to Damien Duff, who cut back on his left foot before swinging over a cross which was met by O'Shea. Unfortunately for the visitors, the former Manchester United defender's header from 12-yards clipped the top of Adam Bogdan's crossbar.
One criticism of Trapattoni's Ireland has been that, whilst they are functional and organised, they lack creation and are very direct, and it was a route one approach which led to their second opportunity after 15 minutes.
A long punt down field by Given was flicked on by Doyle into the path of skipper Keane, but whilst the LA Galaxy forward's angled drive was fierce, Bogdan was equal to it.
A minute later the home side's first effort came, but Dzsudzsak, who was starting to float from his position on the left of Hungary's midfield five, saw his 25-yarder well saved by Given.
The home side were certainly warming to their task and in particular their creator-in-chief Dzsudzsak, who stung the palms of Given again in the 24th minute following some neat passing and a clever lay-off from Szalai.
After 35 minutes Szalai had chance of his own with which he really should have given the hosts the lead. A cross from the left caught out Richard Dunne following a slip but, after good control, Szalai could only strike tamely at Given.
Two minutes before half-time, Szalai had another opportunity. However, having moved onto a pass from Peter Szakaly the forward was denied the opportunity to shoot due to a mixture of his lack of composure and a last-ditch challenge from Stephen Ward.
At half-time both sides made changes, with Vilmos Vanczak replacing Adam Pinter for the home side, and Ireland making a double change, with Keiren Westwood on for Given and Walters replacing Doyle.
Westwood, the Sunderland back-up keeper, quickly had his handling tested by a long-range effort from Joszef Varga, but it was nothing more than a routine stop for the 27-year-old.
However, whilst that stop was run-of-the-mill, that which denied Szalai in the 54th minute was anything but.
Good work down the right saw Szalai tee up Dzsudzsak once more before inadvertently deflecting his team-mate's strike and forcing Westwood into a terrific diving stop down low to his left.
Ireland had become too easy to play through for Trapattoni's liking and from that point the central midfield pairing of Andrews and Whelan - and later Gibson as Andrews' replacement - dropped deeper as they looked to stifle their opponents.
Accordingly, Trapattoni's side showed their defensive resolve and also fashioned chances at the other end as the second half progressed.
Simon Cox and Stephen Hunt came on and both almost played their part in giving Ireland the lead with two opportunities for the away side on the counter-attack.
Firstly, Aiden McGeady played Cox through on goal but his low strike was saved by Bogdan, and a minute later a pin-point cross from Hunt was headed wide by Walters when he really should have hit the target.
Hunt was soon involved at the other end when an Imre Szabics drive had beaten Westwood and the Wolves midfielder had to clear off the line.
Hungary had one final chance to win the match in injury-time, a wonderfully weighted through pass from Szabics setting Kristian Nemeth free, but his attempt at a curling effort went horribly wrong and the ball trickled safely into the arms of Westwood.