As Germany continued to push forward, the U.S defense began to drop deeper and deeper.
And with 10 minutes of the second half played, Germany finally got the breakthrough it had threatened.
Defender Per Mertesacker sent a thumping header towards goal and while Howard managed to beat the ball away, Muller fired home the rebound from the edge of the penalty area.
It was a magnificent strike from Muller, an effort which left Howard with absolutely no chance as it flew through a clutch of players and into the corner of the net.
It put the German joint top scorer at Brazil 2014 alongside home hero Neymar and Argentina's Lionel Messi.
Trailing by a single goal, news began to filter through that Ghana had moved level against Portugal, with Asamoah Gyan canceling out John Boye's first-half own-goal. Gyan is now Africa's all-time leading scorer at the World Cup with six, having passed Cameroon's Roger Milla.
With its future in the tournament hanging by a thread, the U.S. produced a battling performance with former Germany international Jermaine Jones and Kyle Beckerman snarling at the heart of the midfield.
But with 10 minutes remaining, Ronaldo's strike in Brasilia left Ghana with a mountain to climb -- though it wasn't enough to prevent an early trip home for Real Madrid's world player of the year.
That didn't prevent the U.S. piling forward in search of an equalizer though and both Alejandro Bedoya and captain Clint Dempsey came close to scoring at the death.
"We were dominant," said Muller, who scored five goals at the 2010 World Cup, where Germany lost in the semifinals.
"All the Americans did was sit back deep in their own half, and when that happens, it just becomes a patience game.
"But sometimes even I manage to have a bright idea -- I spend the whole day training like I'm obsessed anyway."