However, Mar Saevarsson put through his own net to gift Hungary a point and leave them in pole position to make it through to the knockout stages.
Read below to see how the action unfolded on Saturday evening.
Hello, and welcome to Sports Mole's live coverage of the match between Iceland and Hungary at Euro 2016.
When the draw was made for Euro 2016 in December, the fixture between Iceland and Hungary was probably the least inspiring of all of the 36 group-stage fixtures. However, after their performances on Wednesday, they have put themselves to within a win of doing enough to secure at least third place in Group F and with it, every chance of reaching the last 16. There is still plenty of work to do but both managers will be aware that they are unlikely to have a better opportunity to reach the knockout stages of a major tournament.
RESULT! The full-time whistle has not long gone in Bordeaux and it's Belgium who are the first winners of the day after they coasted past Republic of Ireland. The world's number two side had disappointed against Italy on Monday night but they showed today that the setback was only a minor blip. Catch up with our on-the-whistle report here.
Without further ado, let's take a look at the two starting lineups...
ICELAND XI: Halldorsson, Sævarsson, Sigurdsson, Arnason, Skulason, Gudmundsson, G.Sigurdsson, Gunnarsson, Bjarnason, Sigthorsson, Bodvarsson
HUNGARY XI: Kiraly; Lang, Guzmics, Juhasz, Kadar; Kleinheisler, Gera, Nagy; Stieber, Priskin, Dzsudzsak
As expected, Iceland boss Lars Lagerback named an unchanged starting lineup. However, it will be interesting to see how he instructs his team to approach this match. They played to nullify Portugal's strengths on Wednesday but they will surely adopt a different strategy against a team who possess similar quality in all areas of the pitch.
Before he continue, there are reports emerging of clashes between Hungarian supporters and stewards at the stadium in Marseille. We will bring you more on that as we get it.
Back to the team news and Hungary coach Bernd Storck, quite surprisingly, has made three alterations to his side. Tamas Priskin, Roland Juhasz and Zoltan Stieber have come into the team in place of Szalai, Attila Fiola and Krisztian Nemeth.
These were the scenes earlier this afternoon as the Hungarian contingent descended on Marseille but it appears that emotions have spilled over inside the stadium. There are no pictures from inside the Stade Velodrome just yet but if everyone is already inside the ground, who knows what is happening.
HEAD TO HEAD! Today's fixture represents the 11th time that the two nations have played each other in an international match and as it stands, there is yet to be a draw. Hungary have won seven times with Iceland emerging victorious in the remaining three games. However, there has been just one game in the past 11 years, which ended in a 4-0 triumph for Hungary in 2011.
There's still just over 25 minutes remaining until kickoff in Marseille so why not head over to our dedicated Euro 2016 section? There's plenty of build-up, reaction and match reports to keep you occupied until Iceland and Hungary take to the pitch.
As you are probably aware, Iceland made headline on Wednesday for getting a reaction out of Cristiano Ronaldo after they held his Portugal side to a 1-1 draw. However, comments made by the Real Madrid attacker took nothing away from the performance of the minnows as they announced themselves on the major-tournament stage. It remains to be seen whether they are capable of backing up that result today but one thing is for certain - they are going to enjoy their time in France regardless of the results and that relaxed attitude makes them dangerous contenders. They will look to the creativity of Gyfli Sigurdsson in this contest but expect Kolbeinn Sigborsson to be more involved too. He averages a goal every two goals at international level and if he is given space in the box, he could make Hungary pay.
Despite seeing off Norway in the playoffs, Hungary had been written off by most ahead of this tournament but their 2-0 victory over Austria suggested that they are also relishing the chance to play in front of a wider television audience. Like Iceland, their performance suggested that they wanted to make the most of reaching a major tournament and they are now firm favourites to take a place in the last 16. Changes have been made to the team that started against Austria but that's not necessarily a bad thing. Tamas Priskin, who has been included in attack, has 17 goals to his name in 57 outings while Zoltan Stieber is full of confidence after his delightful finish for their second goal on Wednesday.
PREDICTION! This game will all depend on Iceland's approach. If they play like they did against Portugal, don't expect many goals but if Lagerback acknowledges that this is their best chance of qualification, expect an open game. We are going to go for 2-1 to Hungary but don't be surprised if Iceland come out of the game with the second successive draw.
According to those inside the ground, any trouble that had taken place has subsided, which is good to hear. The stewards deserve a break after having to deal with Russian hooligans last weekend.
The two teams have made their way out at the Stade Velodrome. I don't think we are full to capacity but it's a terrific atmosphere. Both nations are well backed by their supporters.
Iceland get us underway in Marseille.
It's been a composed start form Hungary, who bide their time in their own half before launching an attack down the right. It comes to nothing but it keeps Iceland occupied in their own final third.
Hungary are doing their best to swarm Iceland whenever they lose possession and it is rushing the minnows. They have conceded no shots on goal but they don't look as assured as Wednesday night.
Bit better from Iceland, who are starting to throw themselves into a few tackles to disrupt the rhythm that Hungary have established in these opening eight minutes. Hungary will be pleased with this start, though.
CHANCE! Iceland win the first corner of the match and Sigurdsson's delivery causes all kinds of confusion instead the Hungary penalty area. From the resulting throw-in, the ball eventually finds Bodvarsson but his header is sent over the crossbar from eight yards. He will be disappointed with that.
Despite conceding that chance to Iceland, Hungary are causing their opponents plenty of problems with the combinations that they are putting together inside the final third. They are playing at a much faster pace than Portugal did on Wednesday.
Surely that should have been a yellow card? Priskin turns Arnason around 40 yards from goal before getting upended by the defender. The referee awards the foul but the Icelandic representative receives nothing but a stern finger-wagging from the official. Very lenient.
Iceland need to keep Dzsudzsak off the ball but they allow the Hungary skipper to weave his way into a central position before striking the ball towards goal. The shot is extremely well blocked but that was a warning to the minnows.
Iceland absorb pressure from Hungary before launching a swift counter-attack down the right. They win a corner but two fine defensive headers from Hungarian players get the danger away. We aren't seeing many chances but these two teams are well matched.
Not much to report over the last few minutes. Hungary are continuing to dominate possession but there are signings that Iceland are beginning to frustrate them. The balls into Priskin are becoming more direct, although perhaps they are trying to give their creative players a breather. They have done a lot of running during the opening 24 minutes.
More of the same I'm afraid. Hungary must have had at least 70% of possession in this match but they are doing very little with it. Iceland won't mind at this stage but there will be a time in this match where they need to step up and try to take the game by the scruff of the neck.
CHANCE! What an opportunity for Iceland! A pass from the outside of Sigurdsson's boot appeared to be intercepted by a Hungarian defender but Gudmundsson eased him off the ball inside the penalty area. However, his resulting shot was poor and straight at Kiraly, who made the save with his boot.
That let-off has resulted in Hungary upping the tempo and a neat move is almost finished off by Dzsudzsak. However, just as he was about to shoot across goal, Ragnar Sigurdsson got across to successfully clear the ball for a corner.
SHOT! The resulting set piece was cleared to corner taker Kleinheisler, who bided his time before cutting onto his left foot. He let fly with a shot that was curling towards the far corner but it evaded the far post by a yard or two. Very good effort, though.
PENALTY TO ICELAND!
GOAL! Iceland 1-0 Hungary (Gylfi Sigurdsson)
Iceland take the lead! After Kiraly dropped the ball, chaos ensued and two Icelandic players went to ground. It appears to have been given for a foul on Gunnarsson but Kiraly appeared to foul another Iceland player. Nevertheless, Sigurdsson made no mistake from the spot and the minnows lead in Marseille.
Conceding that goal has riled Hungary and they are back on the offensive as we get closer to the break. As it stands, Iceland are going top of Group F!
There will be one minute of added-on time.
HALF TIME: Iceland 1-0 Hungary
The half-time whistle goes in Marseille and Hungary finds themselves a goal behind after Gylfi Sigurdsson netted with a penalty with six minutes remaining of the first half. It's debatable whether the spot kick should have been awarded but Iceland won't care - they are 45 minutes away from effectively securing a place in the last 16.
Hungary get us back underway. Neither side have made a change.
It appears that Hungary have been told in no uncertain terms to keep playing at a high tempo and their chance will come. A fine ball into the middle from the left flank almost found Priskin but the forward was adjudged to have fouled a defender.
Gunnarsson concedes a cheap free kick around 35 yards from goal. Will Hungary shoot or send in a cross? Dzsudzsak sends in the set piece to the edge of the area - that's definitely something that has been decided on the training ground - but Kleinheisler drilled his effort over the crossbar.
Iceland are barely making the effort to get out of their own half - it's a dangerous game to play this early in the second half. Hungary are building pressure with each wave of attack and although they are yet to get a shot on target, it may only be a matter of time.
CHANCE! Iceland are finally given a break on the ball and they use it to their advantage to win a free kick in the Hungarian half. The ball is floated into the penalty area and although it is headed into the air, Bodvarsson attempts an over-head kick that goes miles into the stands. Well, not quite miles, but you get the idea.
We are through an hour at the Stade Velodrome and despite having just 31% of possession, Iceland remain ahead. It's the kind of game where a second goal may secure the win but if they concede, Hungary would push forward in numbers. It's very finely poised.
There's space starting to open up in the Icelandic final third now but so far, they are holding firm. Priskin is becoming increasingly influential but he may be at risk of being replaced. Interesting to see what their coach does here.
SUBSTITUTIONS! Iceland bring on Emil Hallfredsson for Gunnarsson while Hungary make two alterations, introducing Nikolic and, we think, Bode. Priskin has gone off, which I think is a mistake.
SHOT! Iceland concede a free kick around 25 yards from goal and Dzsudzsak is all over this. His set piece is on target but Halldorsson is able to claim at the second opportunity.
SUBSTITUTION More changes as Bodvarsson is replaced by Alfred Finnbogason. Bodvarsson put in a good shift for Iceland today.
SHOT! Hungary are still looking for that bit of inspiration in attack and Bode tries to provide it with a sharp turn and shot on the edge of the area. Unfortunately for the substitute, his effort is lacking the power to beat the goalkeeper.
SHOT! Hungary's best hope could lie with Dzsudzsak and he agains takes the most interest when a free kick is awarded on the edge of the penalty area. It's a much better effort than his last one but it's straight at Halldorsson, who doesn't have to move from his starting position.
There are just 10 minutes to go in Marseille. Hungary are continuing to press but they are being met by some impressive defending from the minnows. They are edging ever near a tremendous accomplishment.
The referee is dishing out plenty of yellow cards now. I'm struggling to keep up with them! Eidur Gudjohnsen is coming on for Sigborsson, who has run himself into the ground for Iceland.
SUBSTITUTION! Hungary have also made their final alteration with Adam Szalai replacing defender Ronald Juhasz.
Iceland are just trying to run down the remaining minutes now. Hungary may have run out of gas.
GOAL! Iceland 1-1 Hungary (Birkir Mar Sævarsson)M
Disaster for Iceland! Hungary equalise through an own goal from Birkir Mar Saevarsson, who can only divert the ball into his own net after a low cross from Nikolic. It's so harsh on the minnows. There will be four minutes of added-on time.
It's Iceland who are pushing for a winner and they are earned a free kick no know than half a yard outside of the penalty area. Will we have more drama?
Almost! Sigurdsson's free kick is blocked before Gudjohnsen's shot is deflected a yard wide of the post. Game over.
FULL TIME: Iceland 1-1 Hungary
The full-time whistle goes in Marseille and the game has ended in a 1-1 draw. Hungary would have been hoping for three points from today's game but after netting late on, it will feel like a win and they are all but assured a place in the last 16. As for Iceland, they will likely have to beat Austria in the final game so all is not lost.
That will be all from Sports Mole for this game but we hope that you can stick around for the fixture involving Portugal and Austria. Goodbye for now.