The Bayern Munich man opened the scoring from the penalty spot before adding a goal in either half to see Germany open their World Cup campaign with a strong statement of intent.
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"Thomas played very well up front. He kept Pepe and [Bruno] Alves busy the whole time. With his running paths he ripped the defence apart for other players – and he scored three goals. That's Thomas Muller."
The Germany coach also allayed fears over a potential layoff to goalscorer Mats Hummels, who had to be helped from the pitch in the second half with a visible gash on his leg.
"He suffered a blow on his thigh. I don't think it's that dramatic," he revealed.
Low also took time to celebrate Jerome Boateng’s defensive performance on Cristiano Ronaldo, who cut a frustrated figure for most of the game after failing to get on the scoresheet.
"When Ronaldo can start to run, it is going to get difficult because he can score with both feet. If he enters the box it is very dangerous," he explained.
"It was our goal to hassle him when he got the ball. Boateng did that very well. And when Boateng wasn't around, somebody else did."
With Germany a man up and three goals to the good by half time, the 54-year-old was also keen for his side not to over exert themselves during a humid second half in Salvador.
"The team was extremely compact, we did not give away counter attacks. When we had the ball we went up the pitch well. Especially in the first half we played a fast and offensive game and we converted our chances.
"It was a different game in the second half. With this heat and against an opponent with a man down and leading 3-0 it was important to keep the ball and to be energy-efficient."