Christian Eriksen's two penalties kept the hosts in contention for a place at the finals.
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Denmark set up a group decider away to Belgium thanks to two Christian Eriksen penalties in Copenhagen.Denmark vs Iceland: as it happened, reaction
Match in brief
Iceland's hopes of a first ever UEFA Nations League point suffered an early blow when Ari Skúlason felled Daniel Wass and Eriksen thumped in from the penalty spot. There were few further chances at either end until a frantic final five minutes.
Skúlason's slide-rule pass allowed substitute Vidar Kjartansson to equalise but Iceland could not hold on as Hördur Magnússon's handball gave Eriksen the chance to rifle in his 26th international goal in his last 37 games from the spot.
Denmark must now win in Belgium on Wednesday to reach the finals from League A2.
Sture Sando, Denmark reporter
What seemed like a routine day at the office for Denmark had a sting in the tail. Eriksen's added-time penalty was definitely a let-off for his team, who looked to have thrown away a comfortable lead. One worry going forward is the fitness of goalkeeper Kasper Schmeichel. However, coach Kasper Hjulmand's chosen side carried out his game plan and he got to see that they can handle playing three at the back. A player like Mathias Jensen, who wasn't expected to start, did a very good job. Now the 'final' awaits in Belgium on Wednesday, where only three points will do for Denmark.
Andri Yrkill Valsson, Iceland reporter
Two last-minute defeats in four days is hard for any team, but to lose because of two penalties against Denmark at Parken is especially hard to digest for Iceland, particularly because there were a lot of positive signs. The players followed the plan well for most of this match, keeping the defence tight at the beginning and going forward with confidence in the second half. Now it's all about mentality, rising up again before a tough game against England on Wednesday.
Christian Eriksen, Denmark midfielder: "In the first half they sat back a lot. In the second half they were more intense than we were. And in the end, I think we were a bit lucky to score."
Kasper Hjulmand, Denmark coach: "It's a very big achievement to have a final on the final day in a League A group. To have ten points and to go to Belgium for a final – that says a lot about the quality of this group of players and the potential we have in Danish football."
Erik Hamrén, Iceland coach: "I'm really proud, especially after we conceded an early goal. We had to work hard after that because they had the ball more. We were tighter and tougher in the second half and could win the ball more easily. I'm happy with the players, they all showed they really want to play football. They have a fantastic mentality after two tough days. They are fantastic boys to work with."
Sverrir Ingason, Iceland defender: "This is frustrating. We were in a bit of trouble for the first 20 minutes, but in the second half we were able to press them higher up the pitch and scored a great goal. After that I felt we were more likely to grab the win. We felt good out there so it's tough to lose like this."
• Denmark have lost just twice in their last 42 games.
• Denmark have scored in the 84th minute or later in eight of their last 20 matches.
• Denmark have won ten of their last 14 games, only conceding five goals in total.
• Iceland are still looking for their first ever points in the UEFA Nations League (L9).
• Iceland have conceded a total of 26 goals in their nine UEFA Nations League matches.
Denmark: Schmeichel (Rønnow 46); Stryger Larsen, Vestergaard (Wind 90), Kjær, Wass; Delaney, A Christensen, Jensen (Jønsson 68); Braithwaite (Andersen 76), Y Poulsen, Eriksen
Iceland: Rúnarsson; A Skúlason, H Magnússon, Eyjólfsson, Ingason, B Sævarsson; B Bjarnason (Pálsson 46), G Sigurdsson, A Sigurdsson (A Gunnarsson 70); Guðmundsson (Finnbogason 74), Bödvarsson (Kjartansson 70)