In the final, the Greeks were on the back foot in the early stages, with goalkeeper Antonios Nikopolidis being forced into the first save of the game from Portugal's Miguel, but the score remained 0-0 as the half-time whistle blew.
Greece took the lead after 57 minutes, as Angelos Charisteas headed home Angelos Basinas's corner past Portugal goalkeeper Ricardo. Cristiano Ronaldo then immediately forced Nikopolidis into another smart save, but with further chances squandered in the latter stages, Greece managed to hold on for the unlikeliest of victories.
How Greece's triumph compares to other Euro final shocks
Of course, the subsequent years have been far kinder to Portugal; 12 years later, they would have their moment in the sun, while Greece have gone a whole decade without even appearing at a major tournament.
However, the memories will last a lifetime regardless, and here we explore how their achievements compare to other shock results in Euro finals.
Czechoslovakia 2-2 West Germany - Czechoslovakia win 5-3 on pens (1976)
Before the uniting of the nation, Germany was split, with two separate teams representing West Germany and East Germany respectively. It was West Germany that were far more successful, winning as many as three FIFA World Cups and two European Championships - including Euro 1972 four years prior to this match.
As such, West Germany were the holders going into this tournament, and were one of the favourites to win the Euros again, boasting accomplished stars like captain Franz Beckenbauer. In comparison, Czechoslovakia had never won a major trophy before in their history, with their best finish being second place at the 1934 World Cup.
Nonetheless, the underdogs took a 2-0 lead in the final, but were pegged back to 2-2 by West Germany in the latter stages.
That could have dented Czechoslovakia's confidence hugely, but in the resulting penalty shootout, a certain Antonin Panenka stepped up and did something remarkable.
After holding out in extra time, the Czechoslovakian players could have been forgiven for feeling jelly-legged, but they scored all five of their penalties to lift the trophy.
Panenka stepped up to take what would prove to be the winning spot kick, bravely chipping the ball, or 'Panenka-ing' as the term is now known, into the middle of the goal after waiting for goalkeeper Sepp Maier to dive to one of the corners.
Verdict: While beating the reigning Euro champions to earn their first piece of major silverware is no gimme, we feel that Czechoslovakia's achievement is slightly behind that of Greece.
Indeed, they had come close to winning the World Cup before, whereas Greece were huge underdogs and were even priced as high as 150/1 by some bookmakers to win Euro 2004.
The Greeks also did not need penalties to beat Portugal in the final, as they triumphed in normal time. However, Czechoslovakia winning Euro 1976 was still a monumental achievement.
Denmark 2-0 Germany (1992)
Denmark were not initially supposed to compete at Euro 1992, let alone win it. Indeed, they originally failed to qualify for the tournament, but replaced Yugoslavia at short notice, after they were banned due to Resolution 757.
Similar to Czechoslovakia, the Danes had never won any major silverware prior to the tournament, and had never even qualified for the Euros until 1964 or the World Cup until 1986.
However, what they lacked in tournament pedigree compared to the likes of Germany, they made up for with icons that are still revered today. With legendary Manchester United goalkeeper Peter Schmeichel in between the sticks and then-Bayern Munich talisman Brian Laudrup up front, they had quality at both ends.
Despite having a midfield that was unfancied to hold its own against Europe's finest, Denmark progressed to the semi-finals, and knocked out the Netherlands - reigning European champions before the Red and White dynamite blew their defence apart.
Next up came world champions Germany, who were expected to humiliate Denmark, but Schmeichel was heroic, denying star striker Jurgen Klinsmann amongst a raft of saves, giving the Danes a 2-0 win that sent shockwaves around the continent.
Verdict: Considering that Denmark did not initially qualify for Euro 1992 and were given very little time to even prepare, we feel that this may give them the edge over Greece in terms of their achievement.
Their previous best Euros finishes were semi-finals in 1964 and 1984, which suggests that their team may have been better equipped than Greece to go on and win it, but they were up against some real heavyweights of the game at the time.
Nonetheless, Greece's achievement should still not be underestimated, and will still go down as one of the greatest shocks not just at the Euros, but in footballing history.