The first half-chance of the match fell to the home side after four minutes, but Keith Andrews's effort drifted high and wide from just inside the box.
The away side began to dominate possession as the half approached and Thomas Muller twice came close with headed efforts either side of the 20-minute mark.
Germany continued to pass and probe and Sami Khedira was next to come close just before the 30-minute mark, but his effort was blocked by O'Shea.
Germany did take the lead moments later, however, when Reus pounced on a loose ball to fire an effort past Kieren Westwood.
Ireland continued to struggle for invention late in the opening period and Reus scored his second five minutes before the break after good work from Jerome Boateng.