Hungary beat Norway 2-1 in the second leg of their European Qualifier play-off to seal a 3-1 aggregate victory that books them a place at Euro 2016.
The home side's passage to next summer's tournament was never in doubt thanks to Tamas Priskin's early strike, before Markus Henriksen's 83rd-minute own goal sealed matters at the Groupama Arena.
And despite Henriksen grabbing a late goal back for the visitors, Hungary held on to make it through to the finals of a major tournament for the first time since they played at the 1986 World Cup in Mexico, 30 years ago.
If Hungary showed some nerves in the opening exchanges, those were soon over as Priskin fired them in front with a brilliant strike after 14 minutes to send the home fans into a state of delirium.
Running on to Tamas Kadar's hopeful ball down the left-hand channel, the former Ipswich and Watford striker won possession, before cutting in and unleashing an unstoppable shot from the edge of the box that curled into the corner of Orjan Nyland's net for his 17th goal in 54 internationals for his country.
That early strike settled both the home players and the supporters in Budapest, with Bernd Storck's side then passing the ball around with confidence in the opening quarter of the game.
Norway, though, slowly began to gain a foothold in proceedings as the shock of Priskin's strike soon wore off, with the visitors almost drawing level after 27 minutes through Haitam Aleesami.
However, with just Gabor Kiraly to beat, the left back was unable to get the better of the 39-year-old shot stopper from close range, a miss that was to prove crucial come the full-time whistle.
The home side also had further chances to extend their lead, with Gergo Lovrencsics failing to hit the target with a far-post header after being expertly picked out by Laszlo Kleinheisler's inch-perfect left-wing centre.
And Norway very nearly grabbed a crucial away goal in the final minute of the half when Even Hovland rose powerfully to meet Martin Odegaard's left-wing corner, only for his effort to come back off the post.
Both managers made changes at the break, with Hogmo taking off 16-year-old Real Madrid starlet Odegaard, which was a surprise given his side needed two goals to make it to France next summer.
Hungary were always comfortable, however, protecting their two-goal lead and looking to catch their opponents on the counter, which they very nearly did just before the hour, but captain Balazs Dzsudzsak's deflected effort from the right-hand edge of the area clipped the top of the bar.
And the Bursaspor midfielder went close again with 18 minutes to go after a powerful run had taken him through a posse of Norwegian players, but on this occasion he was denied by an excellent save from Nyland.
The visitors had offered very little in attack in the second half, despite their desperate need for goals, their best opening coming when Alex Tettey's scuffed shot from distance deflected into the path of Marcus Pedersen, but Hungary keeper Kiraly was on hand to block smartly.
Minutes later the tie was all but over as the home side doubled their lead when Henriksen inadvertently diverted a right-wing corner past a helpless Nyland via the frame of the goal.
The visitors' stand-in captain did make up for his mistake by pulling a goal back with three minutes left to play after Kiraly had beaten away substitute Jo Inge Berget's effort.
But that proved to be a mere consolation as Hungary booked their first appearance at the European Championships since 1972.