Co-hosts Sweden had maintained their perfect record in the competition on Friday, surviving a real test from Slovenia and securing a four-goal win that kept them top of Main Round Group 2.
But as the competition progressed, it was perhaps only right that the matches would get tougher for the co-hosts, as Omar Ingi Magnusson opened the scoring for Iceland, who wasted little time in building a 3-1 lead.
Albin Lagergren's first goal got Sweden level again at 3-3 in the ninth minute, but that only ushered in a 3-0 run for Iceland, two of which were scored by Bjarki Mar Elisson. Blagult cut the deficit, but Michael Apelgren was forced to take a timeout after Viggo Kristjansson's goal but Iceland 8-5 up.
However, the head coach's words had little effect, as Sweden had no answer to the visitors' attack, as they put together another 3-0 streak past the midpoint in the half to open a five-goal lead at 12-7, before an Odinn Rikhardsson goal in the 22nd extended it to six.
That was an advantage Sweden failed to eat into before half-time, as their ill-discipline and resolute Icelandic defending was keeping them at bay. In the final minute, Lukas Sandell missed two good chances to cut the gap, as Iceland went into the break 18-12 ahead.
Goals from Eric Johansson and Daniel Pettersson either side of a huge Andreas Palicka save to deny Ellidi Vidarsson gave Sweden the perfect start to the second half, but after the sides traded goals, it wasn't until a Johansson rocket after 40 minutes that the Swedes cut the lead to three - 21-18.
However, the Malmo Arena crowd were on their feet again moments later when a spectacular Palicka save set up an attack, finished off by Lagergren and suddenly the gap was just two. Gisli Kristjansson then burst through the Swedish defence in response, but his shot crashed against the post, sending Sweden up the other end, and Felix Claar made no mistake in making it 21-20.
But where Gisli failed, Viggo was staying perfect - he scored his 11th goal from 11 attempts to help relieve the pressure on Iceland, who made it a three-goal game again going into the final 12 minutes.
As the minutes ticked by, it was looking like Sweden had missed their best chance to draw level, as an unorthodox Viktor Gisli Hallgrimsson save, plus goals from Magnusson and Rikhardsson grew the advantage back to four, as only Palicka's saves kept Sweden in the tie.
Iceland were all but over the line when they put together a 5-0 run in the last 10 minutes - the best run of the match for either side - with Elisson playing a key role with one goal from a fastbreak and another from the wing, while Hallgrimsson remained completely unbeatable.
Elisson had the final say with his sixth goal of the game to make the final score 35-27 to Snorri Gudjonsson's Iceland, as Viggo Kristjansson top-scored with 11 goals, while Lagergren was Sweden's best shooter, with five goals.
Following a one-goal loss to Croatia to open the Main Round, the victory was vital for Iceland to keep their last-four hopes alive ahead of their meeting with Switzerland on Tuesday. Sweden will hope to bounce back and stay in control of their destiny when they play Hungary, also on Tuesday.