Gomez is coming off his best season and the 25-year-old scored his 16th goal in his 44th international appearance, having scored 28 times for Bayern in the Bundesliga to finish as the German league's top scorer.
"We started well and played with a high tempo in front of goal," said Gomez. "We created two nice goals, but we will have to do more (to win in Vienna)."
Germany now face qualifiers for EURO 2012 against Austria, in Vienna on Friday, and Azerbaijan in Baku on 7 June. They already have one foot in the finals, though, having won all five of their opening Group A encounters. Uruguay are preparing for the Copa America which will be held in Argentina in July.
Just as they had done in Port Elizabeth, Germany ran out winners, but this time the hosts were without both injured midfielders Sami Khedira and Bastian Schweinsteiger. Germany coach Joachim Loew fielded an experimental midfield with veteran Simon Rolfes of Bayer Leverkusen alongside youngsters Toni Kroos and Schuerrle.
Germany take the lead
After a dull start to the game, the match burst into life in the 20th minute when Gomez robbed Fenerbahce defender Diego Lugano of possession just inside the Uruguay half. He then beat two defenders and drew the goalkeeper before rifling his shot home for a superb individual goal.
The hosts extended their lead when Schuerrle, winning only his third cap, slotted home his first goal for his country on 35 minutes when Real Madrid winger Mesut Ozil found a hole in the guests' defence. Schuerrle smashed home an unstoppable shot from the edge of the penalty area.
But Uruguay were denied a goal when Germany Manuel Neuer made a hash of a shot by Atletico Madrid's Diego Forlan and spilled the ball into his own net, but luckily the linesman ruled offsides to keep it 2-0 at the break.
The South Americans pulled one back when Napoli midfielder Gargano made no mistake directly in front of goal and punished the German defence just after half-time to breath life back into the game. With Ozil off, Germany's attack struggled to impose themselves while Uruguay had a few chances to equalise as the game wore on.
Uruguay coach Oscar Tabarez made just two changes to his side, while Loew took the opportunity to experiment, bringing on six replacements, including Mario Goetze, who only turns 19-years-old next week. Goetze had a chance to score Germany's third in the dying stages, but failed to chip his shot over Uruguay goalkeeper Fernando Muslera of Lazio.