Match ends, Iceland 1, Hungary 1.
Birkir Saevarsson's late own goal denied Iceland a famous victory as Hungary edged towards the last 16 of the European Championship with a draw.
Gyfli Sigurdsson gave Iceland the lead in the first half when he converted a penalty after a foul.
Hungary dominated possession from then on but found themselves repeatedly frustrated by the Iceland defence.
However, Saevarsson turned Nemanja Nikolic's cross into his own net to hand Hungary a point.
The result means the Hungarians are top of Group F with four points and can clinch first place with victory against Portugal in their final group game on Wednesday.
Iceland's defence a tough nut to crack
The point for Iceland means they are second in the group and remain in the hunt for a place in the last 16, but it will feel like a defeat after they frustrated Hungary for so long.
They had won plenty of new fans by holding Portugal to a 1-1 draw in their first game on Tuesday, a result that prompted some scathing comments from Cristiano Ronaldo, who descried the Icelanders as having "a small mentality" and playing only to defend.
Iceland, though, are simply playing to their strengths. They conceded only six goals in 10 games during qualifying, earning wins by making the most of limited opportunities.
On Saturday, the Hungarians found themselves continually frustrated by a well-organised and disciplined backline and their task got harder six minutes before half-time. Veteran goalkeeper Gabor Kiraly fumbled a cross, Gunnarsson was sent to the ground by Kadar inside the area and Sigurdsson kept his cool to send Kiraly the wrong way from the spot.
From then on, it was all Hungary but it looked as if Iceland's defence would triumph again until Saevarsson, under pressure from Hungary substitute Daniel Bode, poked beyond his own goalkeeper.
It continued a run of late drama at Euro 2016, with Saevarsson's unfortunate goal the 13th to come after 85 minutes.
Kiraly can play better
Hungary ended a three-decade run of missing out on major tournaments by qualifying for Euro 2016, and they made up for lost time with an impressive 2-0 win over Austria in their opening group game.
Having beaten Iceland in each of their past five meetings, they will have gone into the game confident of securing successive wins at a major tournament for the first time since the 1966 World Cup.
Gabor Kiraly caught the eye against the Austrians, both for his attire and his saves, as he became the oldest player to play at European Championship finals at the age of 40 years and 75 days,
However, he was less impressive on Saturday, putting his defence under pressure with poor passes before flapping at the ball to add to the panic that led to Iceland's penalty.
It was a nervy performance by the former Crystal Palace man, who will need to improve when facing Ronaldo and colleagues in Hungary's final group game against Portugal.
Man of the match - Gylfi Sigurdsson
The stats you need to know
- Hungary conceded their first penalty goal in European Championship history in this match.
- Five of Gylfi Sigurdsson's last seven goals for Iceland have come from the penalty spot.
- Birkir Saevarsson scored an own goal in this match, the second of this tournament. The last time there were as many at the Euros was in 2004 (2).
- Eidur Gudjohnsen (37y 276d) became the fifth oldest outfield player to play at the Euros after Lothar Matthäus, Morten Olsen, Ivica Vastic & Ricardo Carvalho.
- Hungary are unbeaten in six internationals against Iceland (W5 D1).
- This is the first time the two nations have drawn with each other (Hungary hold seven wins to Iceland's three).
- Iceland have only lost once across their last eight competitive matches (W3 D4).
Hungary play Portugal in Lyon on Wednesday and three points will secure first place in Group F. Iceland, meanwhile, face Austria in Paris on the same day.
- 2SaevarssonBooked at 77mins
- 6R Sigurdsson
- 23AF Skúlason
- 7Berg GudmundssonBooked at 42mins
- 17GunnarssonSubstituted forHallfredssonat 66'minutes
- 10G Sigurdsson
- 9SigthorssonSubstituted forGudjohnsenat 84'minutes
- 15BödvarssonSubstituted forFinnbogasonat 69'minutesBooked at 75mins
- 23JuhászSubstituted forSzalaiat 85'minutes
- 4KádárBooked at 81mins
- 15KleinheislerBooked at 83mins
- 8NagyBooked at 90mins
- 19PriskinSubstituted forBödeat 66'minutes
- 18StieberSubstituted forNikolicat 66'minutes
- Sergey Karasev
- Shots on Target
Second Half ends, Iceland 1, Hungary 1.
Attempt blocked. Eidur Gudjohnsen (Iceland) right footed shot from the centre of the box is blocked.
Attempt blocked. Gylfi Sigurdsson (Iceland) right footed shot from outside the box is blocked.
Foul by Adám Lang (Hungary).
Alfred Finnbogason (Iceland) wins a free kick in the attacking half.
Attempt saved. Ádám Szalai (Hungary) right footed shot from outside the box is saved in the centre of the goal. Assisted by Dániel Böde.
Richárd Guzmics (Hungary) wins a free kick in the defensive half.
Foul by Alfred Finnbogason (Iceland).
Adam Nagy (Hungary) is shown the yellow card.
Foul by Adam Nagy (Hungary).
Alfred Finnbogason (Iceland) wins a free kick in the defensive half.
Own Goal by Birkir Saevarsson, Iceland. Iceland 1, Hungary 1.
Foul by László Kleinheisler (Hungary).
Eidur Gudjohnsen (Iceland) wins a free kick in the defensive half.
Substitution, Hungary. Ádám Szalai replaces Roland Juhász.
Offside, Hungary. László Kleinheisler tries a through ball, but Dániel Böde is caught offside.
Substitution, Iceland. Eidur Gudjohnsen replaces Kolbeinn Sigthorsson.
László Kleinheisler (Hungary) is shown the yellow card.
Foul by Nemanja Nikolic (Hungary).