Goetze took a pass from the left from Andre Schurrle in the 113th minute of action, trapped it on his chest and swiveled it past Sergio Romero and into the Argentina net. The goal proved to be enough to give Germany a 1-0 victory.
"For us, it really is a dream come true," Goetze said. "I'm more than happy and I'm happy with the team and what happened here in Brazil. I guess it's more or less indescribable how I feel. It is absolutely sensational."
It was tense and cagey and royally entertaining. And it was sealed by a 22-year-old who had come on as substitute for Miroslav Klose with just two minutes of regulation time remaining.
Goetze's strike was the first time Argentina had trailed in the entire tournament and sent his nation into delirium, securing its first world title since 1990.
For Argentina it was agony. Lionel Messi and his team came so close but it wasn't enough. In the end, the Germans were too strong, too clinical, and in every way the best all-round collection of players at this event.
Argentina had the best early chance, the kind that leaves forwards holding their head if they miss them. This time the unfortunate man was Gonzalo Higuain, who was sent through by an ill-conceived backward header from Germany's Toni Kroos. But Higuain scuffed his shot completely with only Manuel Neuer to beat.
Soon after Higuain did manage to put the ball in the net, to the temporary delight of the Argentinean support, only for it to be correctly whistled back for offside.
Germany's possession game was slick and sharp but missing a little extra ingredient. Sami Khedira had been ruled out through a late injury, then his replacement Christoph Kramer went down with a sickening head clash midway through the first half, bringing Schurrle into the fray.
The Germans should have gone ahead on the stroke of halftime, with Benedikt Howedes surging forward to aim a powerful header at goal, only for his effort to crash against the post with Romero beaten.
While Messi toiled and teased in the second half it was Germany that was taking control and Toni Kroos, one of the players of the tournament, marked an uncharacteristically sloppy display with a tame shot with nine minutes of normal time to go.
Extra time sometimes gets bogged down into cagey stalemate, but not so on this occasion. In the very first minute of the additional period, Schurrle's strike on target had to be pushed away by Romero to quicken pulses on both sides.
The pace did not slacken, not a bit. It was relentless; Sergio Aguero broke clear at the other end and foolishly tried to shoot from an angle instead of cutting back, while substitute Rodrigo Palacio, on for Higuain, went clear minutes later but skewed his attempted lob over Neuer but wide of net.
Penalties had been used as a decisive factor in the World Cup final just twice before – when Brazil beat Italy at the Rose Bowl in 1994 and when Italy defeated France following Zinedine Zidane's infamous headbutt in 2006. Just when potential takers were being discussed around the iconic Maracana Stadium it was time for Goetze, one of Europe's most heralded youngsters, to step up. He stepped quickly to move clear of the defense, with balance to steady himself – and forwards, into history.
"I told them before the match that you will have to give more, more than you've ever given before, to achieve something you've never achieved before," German coach Joachim Loew said. "And that is to take the Cup home."