The Bayern Munich midfielder took his overhaul tally of World Cup goals to nine in the same number of appearances with strike number four in Brazil.
That was enough to earn Germany top spot in Group G, and a place in the last 16.
“We were dominant,” said Muller. “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.”
That idea was a pinpoint low strike from the edge of the penalty area which decided the game in Germany’s favour.
“It was an okay game from us,” added Muller to Germany’s ZDF television. “We may only have won it 1-0, but we can take that too.”
Only in stoppage time did Jurgen Klinsmann’s men come close to breaching the Germany defence, but Philipp Lahm stepped in to block Alejandro Bedoya’s effort.
It was an otherwise quiet day at the office for the Germany rearguard.
Klinsmann could not hide a grin at the final whistle either. The result gave him double cause for celebration as the USA joined his native Germany in the last 16.
“We created too few chances, but it’s still fantastic to go through,” said the man who led Germany to third place at the World Cup in 2006 before stepping aside to let Low take over.
“Everybody said we had no chance, but we’ve taken it and we’re now in the last 16.”
USA: Howard, Johnson, Gonzalez, Besler, Beasley, Beckerman, Jones, Zusi (Yedlin 83), Bradley, Davis (Bedoya 59), Dempsey.
GERMANY: Neuer, Boateng, Mertesacker, Hummels, Howedes, Schweinsteiger (Gotze 76), Lahm, Kroos, Ozil (Schurrle 89), Muller, Podolski (Klose 46).
Referee: Ravshan Irmatov (Uzbekistan).