Nils Petersen scored five and Maximilian Meyer three as the Germans ran riot against a side making their first appearance in a top international football tournament.
Their win lifted them above the Mexicans, who lost 1-0 to South Korea by conceding a goal to Kwon Chang-hoon in the 77th minute.
The results left the Koreans top of Group C with seven points and Germany second with five. Mexico, who beat Brazil to win the gold in London four years ago, were eliminated along with Fiji.
South Korea will play Honduras and Portugal face Germany. The top two teams in each of the four groups go through to Saturday's quarter-finals.
Champions in their last two Olympic tournaments in 2004 and 2008, Argentina missed a penalty that would have taken them through but an injury time equaliser against Honduras, who scored one penalty and missed another, was not enough.
The Argentines, who did not qualify for London 2012, finished behind Group D winners Portugal and Honduras in the standings. The Portuguese drew 1-1 with Algeria.
Four more games will be played later on Wednesday to decide the other quarter-finalists.