The Three Lions, who had earlier stuttered through Group B in finishing second, edged ahead inside four minutes but saw their lead quickly evaporate in a defeat that ultimately cost under-fire boss Roy Hodgson his job.
It means England have still won just six knockout fixtures in the past 50 years - the last of which came exactly a decade ago when beating Ecuador in the 2006 World Cup.
Iceland, on the other hand, competing in their first ever match of this do-or-die magnitude, have now lost just one of their last 10 outings and face an iconic quarter-final fixture with hosts France at the Stade de France on Sunday evening.
Raheem Sterling, given a reprieve of sorts by boss Hodgson when named in the starting lineup, paved the way for England's opener when using his pace to get on the end of a long ball and going to ground under a challenge from Hannes Halldorsson.
Referee Damir Skomina, often accused of being too reserved when it comes to making big decisions in the past, had little choice but to point to the spot for Wayne Rooney to successfully fire his side ahead.
It was the start that Hodgson would have dreamed of, forcing Iceland - a side ranked at 34 in the world pre-tournament - to come out of their shells in search of an equaliser.
Incredibly, it took just 34 seconds for the Nordic nation to offer up a response as one of the key weapons in Iceland's arsenal, an Aron Gunnarsson long-throw, was headed into the path of Ragnar Sigurdsson to successfully volley past Joe Hart from close range.
England managed to find some momentum once more, just like they had done in the minutes before edging ahead, and they came close to scoring their second when Dele Alli blasted narrowly over from a half-cleared corner.
It was Iceland who found the game's third goal, though, with a fine team move that began with Gunnarsson spraying a pass out to the right and culminated with it being moved into a central position for Kolbeinn Sigthorsson - more known for his aerial ability - to unleash from range.
Hart really should have done better, simply allowing the ball to squirm past him to his bottom left, much like with Gareth Bale's free kick earlier in the competition.
As expected, England came out fired up in the early stages of the second half but were still desperately struggling to find any prolonged spells of momentum as they chased down a goal.
Goalscorer Sigurdsson came close to piling on the misery when his overhead kick was heading for the back of the net if not for Hart's intervention, while at the other end Alli shinned over one of a few half-chances the Three Lions created before the hour.
Hodgson turned to Vardy with an hour of the match played, and the Leicester City title winner nearly made a telling difference when bursting through, only for Sigurdsson's defensive challenge to thwart him.
Kane had one headed attempt kept out in the final 10 minutes, yet Gunnarsson could have sealed things with time to spare when using his remaining energy to burst up the field and firing away a shot that Hart did well to turn aside.
In the end England simply did not create enough chances to get anything out of the game, meaning victory for Iceland at the Stade de Nice - the scene of the nation's finest ever moment.