The tournament’s outstanding team failed to repeat the fluency and brilliance of their 7-1 semi-final romp against Brazil but Joachim Low’s team found one more sumptuous moment during the second half of extra time.
Bayern Munich playmaker Gotze, on as an 88th-minute replacement for World Cup record goalscorer Miroslav Klose, chested down Andre Schurrle’s floated left-wing cross at the near post to superbly steer home from six yards.
It was the first time Argentina had found themselves behind in the competition and it came as a bitter pill to swallow after Alejandro Sabella’s men had created the better chances in normal time.
Gonzalo Higuain passed up a glorious opportunity midway though the first half and the Argentina striker also had a first-half effort correctly ruled out for offside.
Germany defender Benedikt Howedes then headed against the post on the stroke of the interval, and after the break passions threatened to boil over in what was an understandably feisty encounter.
Lionel Messi fired agonisingly wide shortly after the restart, while Germany goalkeeper Manuel Neuer was lucky not to be punished for clattering a knee into Higuain’s face as the striker ran through on goal.
Neuer’s opposite number, Sergio Romero, denied Schurrle inside the first minute of extra time, while fellow substitute Rodrigo Palacio fluffed his lines at the other end before Gotze sealed Germany’s fourth World Cup triumph.
The newly crowned champions were forced into an 11th-hour change after influential midfielder Sami Khedira suffered the heartbreak of sustaining a calf strain during the warm-up.
Borussia Monchengladbach’s Christoph Kramer came in for the Real Madrid man, despite having only played 12 minutes during the tournament and being absent from Low’s provisional 30-man squad before replacing Andre Hahn.