Iceland took the lead thanks to an emphatically struck first-half penalty from Gylfi Sigurdsson after captain Aron Gunnarsson was bundled over in the box.
They couldn't hold on though, and Hungary equalised thanks to a Birkir Saeversson own-goal in the 88th minute after the pressure piled on the Icelandic goal finally paid off.
The draw takes Hungary to four points from their two fixtures, and they are now in with a very strong chance of reaching the knockout stages, while Iceland will likely need something from their final fixture.
Hungarian forwards continue to impress following Austrian triumph
Following impressive opening performances at the tournament, where Hungary beat Austria, and the Icelandics held Portugal to a 1-1 draw, the match in Marseille gave both sides the opportunity to put one foot in the knockout stages.
Both teams had free headers in the opening quarter-hour, but strikers Jon Dadi Bodvarsson and Tamas Priskin each lifted their efforts over the bar.
The Hungarians then started to come into the game much more, with attacking players Balazs Dzsudzsak and Laszlo Kleinheisler really imposing themselves on the game. Dzsudzsak put in a couple of teasing crosses, yet his teammates could not direct their headers goalwards.
Nordics start to create chances, before Sigurdsson puts them ahead from the spot
For all the pressure Hungary were starting to build-up, it was Iceland who were creating the better chances. Charlton Athletic winger Johann Gudmundsson should have scored after being put through one-on-one with Gabor Kiraly, yet the keeper managed to block the goalbound shot with ease.
Kiraly soon became the villain of the piece, after his mistake led to the opening goal. The 40-year-old dropped a corner, which saw the ball break to Gunnarsson, who was tripped by Tamas Kadar.
Russian referee Sergei Kasarev decided that there was enough contact to award a penalty, giving Iceland the chance to take the lead.
Swansea's Gylfi Sigurdsson never looked like missing, sending Kiraly the wrong way with his penalty to put his side one-up, which Iceland held onto until the half-time whistle.
Szalai entrance finally brings equaliser after Hungary had looked destined for defeat
Hungary were in the ascendancy for much of the second-half and were chasing the equaliser, yet never really created the chances their possession and territory demanded.
The ball didn't drop to them in the box, and at the other end Kiraly was almost an observer with Iceland barely leaving their own half.
Having dropped Adam Szalai despite his goal in the opening game, Bernd Storck finally decided to throw on his striker with six minutes left on the clock and the weight of numbers in the box finally paid off.
Having already made his presence felt in the box, the ball came forward again, and a ball across the six-yard box was put into the back of his own net by Saeversson sparking scenes of delight in the Hungarian end.
The late goal could have seen Iceland fall apar and concede another, but it was them who pushed forward and nearly reclaimed the points with the final kick. A blocked Sigurdsson free-kick fell to Eidur Gudjohnsen, with the veterans shot just deflected wide of the post as Kasarev blew his whistle for full-time.