The England striker remains the only man to have scored three goals in a World Cup final.
The match was not without controversy, as a Russian linesman awarded England their third goal after the ball hit the bar and bounced onto the ground.
TV replays failed to prove if the ball had crossed the line, and 36 years after the event it remains a major talking point.
Hurst's finale inspired one of the most famous pieces of commentary of all time, from the BBC's Kenneth Wolstenhome.
As the West Ham striker raced clear to score England's fourth, Wolstenhome said: "Some people are on the pitch, they think it's all over...it is now."
A dispute over the qualification process meant 16 African nations refused to take part, but Portugal were among those who did so for the first time.
And their star player, Eusebio, emerged as the tournament's top scorer with nine goals.
After his injury problems four years earlier, Pele was back for Brazil, but again he was roughly treated and injury forced him out of the tournament once more.
England opened the finals with a boring 0-0 draw against Uruguay, but things livened up when Brazil began the defence of their title with a 2-0 win over Bulgaria at Goodison Park.
However, with Pele missing their next match against Hungary, and limping out of the decider against Portugal, Brazil lost both games and were knocked out.
In Pele's absence the public warmed to the skills of Eusebio, who scored four times as Portugal fought back from three down against North Korea to win 4-3.
After their slow start England beat Mexico and France to top their group and set up a quarter-final against Argentina.
England beat the South Americans 1-0 but the match was played in a bad spirit.
It was held up for 10 minutes when Argentina's captain, Antonio Rattin, was sent off and refused to go, before he was finally dragged away.
England faced Portgual in the last four, and although Eusebio scored yet again the hosts won 2-1 to set up the final with West Germany.
The Germans took an early lead but goals from Hurst and Martin Peters meant England led 2-1 with less than a minute to play.
However, Wolfgang Weber equalised to send the game into extra-time.
England manager Alf Ramsey told his deflated players that they had already won the game once and to go out and do it again.
So they did, with the Russian linesman confirming Hurst's effort to make it 3-2, before the striker completed his hat-trick to finish the game off.
Group 1 results:
England 0-0 Uruguay
France 1-1 Mexico
Uruguay 2-1 France
England 2-0 Mexico
Uruguay 0-0 Mexico
England 2-0 France
Group 2 results:
West Germany 5-0 Switzerland
Argentina 2-1 Spain
Spain 2-1 Switzerland
West Germany 0-0 Argentina
Argentina 2-0 Switzerland
West Germany 2-1 Spain
Group 3 results:
Brazil 2-0 Bulgaria
Portugal 3-1 Hungary
Hungary 3-1 Brazil
Portugal 3-0 Bulgaria
Portugal 3-1 Brazil
Hungary 3-1 Bulgaria
Group 4 results:
USSR 3-0 North Korea
Italy 2-0 Chile
North Korea 1-1 Chile
USSR 1-0 Italy
North Korea 1-0 Italy
USSR 2-1 Chile
Portugal 5-3 North Korea
England 1-0 Argentina
West Germany 4-0 Uruguay
USSR 2-1 Hungary
West Germany 2-1 USSR
England 2-1 Portugal
3rd/4th place play-off:
Portugal 2-1 USSR
World Cup Final:
England 4-2 West Germany (aet)