Germany top the group and will face the runner-up in Group H while the United States finish second and will face Group H's winner. Portugal who beat Ghana 2-1 are eliminated with the Africans.
The Germans dominated the game with Juergen Klinsmann's team, with their backs against the wall, creating very few chances.
The breakthrough came after 55 minutes when Tim Howard parried out a Per Mertesacker header but Mueller collected the loose ball on the edge of the area and superbly side-footed into the bottom corner.
"For once I scored a beautiful goal. If I don't watch out I'll become a legend? OK, I won't watch out," Mueller told ZDF Television after being told he had outscored Diego Maradona in World Cups.
"We are ready for the knockout stage. We keep working hard and we are full of team spirit."
The game had been threatened by a torrential downpour in the north-eastern city of Recife on Thursday morning but the heavy rain that hampered the preparations of fans and players alike eased to a drizzle as kickoff approached.
Despite the fact that both sides only needed a draw to qualify there was no shortage of attacking intent in the lively opening exchanges, with Mueller going close early on from Lukas Podolski's low cross.
Both sides flew into challenges in the battle for supremacy in midfield, and U.S. coach Juergen Klinsmann and his German counterpart Joachim Loew will be glad the referee didn't wave the yellow card more often as they head for the knockout stages.
Content to concede possession for long periods, the Americans put in a blue-collar defensive performance, breaking forward when the opportunity arose, but with their superior technique and ball movement, the Germans were always a threat.
The Americans had several chances of their own but lacked the pace and guile necessary to unduly worry German goalkeeper Manuel Neuer.
"Everyone said we had no chance, but we took the chance and we move on and now we really want to prove a point," U.S. coach Klinsmann said.
"The commitment was great, I wish we had more possession and created more chances but maybe we are saving that for the next one.
"It is huge, huge step and now we can't wait for the round of 16."
source: www.abs-cbnnews.com
