Portugal finished third in the group behind Iceland, but also advanced to the last-16 as one of the best third-placed teams.
The Iberians knew going into their match with Hungary that nothing less than a win would be good enough for them to top Group F, with Nani and Mario both missing glaring opportunities early on, much to the consternation of Cristiano Ronaldo.
They were made to rue their misses even more in the 20th minute as Zoltan Gera ran on to a poor clearance header to half-volley a thundering low drive into the bottom corner to give Hungary the lead.
The sides traded blows after the goal, but it was Portugal who looked more likely to make something happen, as Ronaldo had two free-kicks saved by Gabor Kiraly.
However, Ronaldo was the provider as he threaded a delightful diagonal throughball for Nani, who finished expertly low and hard to make the score 1-1 in the 42nd minute.
Any hope the Portuguese took into half time from the goal was quickly eroded as Balazs Dzsudzsak took a pot shot from a free-kick and it took a deflection past a helpless Rui Patricio to restore Hungary's lead two minutes after the break.
Three minutes later, Ronaldo, who had looked increasingly frustrated all game, finally managed to make an impact for his team at the Euros as he got in front of his marker to execute a deft backheel past Kiraly and get his side back on level terms once again.
But that didn't last long either as, five minutes later, Dzsudzsak rode his luck once again dribbling past two men before attempting a shot from the edge of the area, which was also deflected beyond Patricio to make it 3-2 in the 55th minute.
Unfortunately for Hungary, Ronaldo had found his goal scoring touch by this stage and he rose above the defence to meet a Ricardo Quaresma cross and power the ball home to restore parity for Portugal for the third time in the game in the 62nd minute.
Hungary weren't content with a point and marched down the other end of the pitch as Akos Elek toe-poked the ball agonisingly into the post.
The approach gave Portugal too much space and they began to take control of the game. The whole of Hungary would have had their hearts in their mouths around the 75th minute when they saw a looping cross fall to Ronaldo, but they breathed a heavy collective sigh of relief as the Real Madrid man hit the ball straight into the ground and it bounced over the bar.
Ronaldo tried one last long-range effort late on but Kiraly watched it fly harmlessly past his post.