The 22-year-old attacking midfielder scored in the 113th minute, volleying in the game-winning goal against Argentina in the World Cup final.
His goal gave his country its fourth title, but only its first as Germany. It won three times as West Germany.
Germany's win was also the first for a European team in a World Cup played in South America.
The game had plenty of drama. Surprise starter Christoph Kramer was taken off in the 31st minute after suffering an apparent head injury in a collision earlier in the game. He had replaced starting midfielder Sami Khedira, who injured himself in warm-ups.
Argentine striker Gonzalo Higuain missed two golden chances to give La Albiceleste a first-half lead. He mishit a backwards header by Germany's Toni Kroos that left him one-on-one with goalkeeper Manuel Neuer and also had a goal called back for offside.
Germany's Benedikt Howedes nearly scored before halftime, skying in for a header that rang off the post.
Argentine star Lionel Messi missed a chance early in the second half, sending a curving shot just wide of the far post. He also skied a free kick over the goal in the final seconds.