His replacement, Schurrle, then tested Romero in the Argentine goal with a well struck shot after Mueller got clear on the left. The danger then appeared at the other end when Messi's sprint and driving run into the box got him round the back of the German defence to beat Neuer, although Jerome Boateng scrambled the ball clear. 
Romero saved from Kroos, Mueller sent a curling shot wide and then Hedwiges crashed a header off the woodwork in the shadows of half time as this game really caught fire.
Messi had a wonderful opportunity to put Argentina ahead shortly after the restart when he was played clear in the penalty area, but once again he pulled his shot wide of Neuer's left post.
Neuer, renowned for his expertise as a ''sweeper keeper'', then had to be out off his line smartly to punch clear a long ball as Higuain chased the pass down, the German collecting the striker in the head with his knee as he jumped. 
While Higuain protested, the goalkeeper was entitled to go for the ball and he did reach it before the Argentinian. Whether he should have done so leading with his knee is another issue, and his challenge evoked comparisons with the far worse one by another German goalkeeper, Toni Schumacher, in the 1982 World Cup, when he knocked out Frenchman Patrick Battiston.
As the clock ticked by, the issue of fatigue began to raise itself. Germany's stroll in the park on Tuesday against Brazil would hardly have taken anything out of them, while Argentina, who played a day later against The Netherlands in the other semi final, had to go through 120 minutes and a penalty shoot out, a game which their coach, Alejandro Sabella, described as a ''war''.
The ever combative Javier Mascherano, the heartbeat of this Argentine side, found himself in the book for a late challenge on German striker Mirolav Klose, and moments later Sergio Aguero met the same fate for a late challenge on Bastian Schweinsteiger as the cautions began to mount.
Messi danced around the edge of the penalty area  before getting off another shot that curled just wide. This was Argentina's Achilles heel: they were creating openings, but rarely could they trouble Neuer with a shot on target.
Both coaches rang the changes, and Klose received a warm ovation when he was replaced with just minutes left by Goetze. Klose became the all-time World Cup leading scorer when he struck against Brazil, and at 36 a World Cup final appearance was a fitting end to a marvellous career.
The pace did not let up at the start of extra time as Schurrle sent in a shot that was easily dealt with by Romero while at the other end Neuer tidied up Aguero's cross after a swift Argentine break.
Substitute Rodrigo Palacios came agonisingly close with a lob that beat Neuer but went wide of the post as Argentina continued to threaten from quick counter attacks.
It looked as though it was heading for penalties - before Goetze's wonderful finish.
Klose caps a brilliant international career with a World Cup winners medal, while Messi is left to reflect on the fact that he could not quite inspire his country to a World Cup win in the manner of his predecessor, Diego Maradona, against Germany in 1986.