Muller broke the deadlock with a penalty 12 minutes into their FIFA World Cup opener in Salvador and put the gloss on the victory with two further goals after Mats Hummels had doubled the lead with a header.
However, the 24-year-old was also involved in a moment of controversy as Portugal centre-back Pepe was shown a straight red card with the score at 2-0 in the 37th minute.
Pepe pushed his head into Muller after the Bayern Munich man reacted theatrically to the Real Madrid defender's arm hitting his face in a tussle for the ball, leaving Serbian referee Milorad Mazic with little choice but to reduce Portugal to 10 men.
But Low was thrilled with Muller's overall performance, which puts Germany in a strong position to finish at the top of Group G.
"Thomas did a great job," Low told ARD.
"He kept the defence busy, opened up gaps and scored three goals - that's Thomas Muller."
The 54-year-old also earmarked defenders Jerome Boateng and Hummels, who picked up a knock in the second half, for praise.
"The team was compact, kept the line, did not allow Portugal a lot of chances," Low added.
"Our goal was to attack Ronaldo from the moment he got the ball. Jerome Boateng did a great job.
"Mats Hummels offers a weapon in our attack because he runs with the ball. That goal also came at a great time. A 1-0 lead always is risky - the opponent still has hope."
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