Joachim Low's side dominated large swathes of the match and were rewarded with a goal in either half at a sodden Red Bull Arena in East Germany.
Bayern Munich's players all came into the side having been given time off following the Champions League final with goalkeeper Manuel Neuer, Holger Badstuber, Philipp Lahm, Toni Kroos, Thomas Mueller, Mario Gomez and Jerome Boateng all starting. However, Bastian Schweinsteiger is carrying a calf injury and was not risked.
Having lost 5-3 to Switzerland in Basel in a friendly on Saturday, Germany resorted to a more familiar line-up and got their reward five minutes before the break when Bayern's Gomez buried the ball high into the net from 10 yards out after being played in by Mueller, who had been set up by Real Madrid's Sami Khedira.
Substitute Andre Schuerrle added a brilliant second in the Leipzig rain when he drove the ball beyond visiting goalkeeper Ariel Harush from 25 yards out to put the outcome of the evening beyond doubt on 82 minutes.
Germany were always the likelier side with seven Bayern players in their starting line-up as Harush saved from Gomez in the first period and Boateng drove a shot off a post.
Gil Vermouth forced Neuer to make a fine stop on 54 minutes as he swatted a shot over the bar while Mueller should have scored for the home side when he slipped an effort wide of goal before Leverkusen forward Schuerrle struck with some style to give Germany a winning send-off.
Germany open their Euro 2012 campaign against Portugal in Group B in the Ukraine city of Lviv on June 9 before facing the Netherlands (June 13) and Denmark (June 17) in their other group matches at the finals.
They are attempting to win their first European title since 1996, but are buoyed by a final appearance in Euro 2008 and the semi-finals of the 2010 World Cup with tournament winners Spain accounting for them on both occasions.