Lahm put in a captain's performance, and it was his interception from an ambitious Irish pass that set up Khedira to score.
It seemed just a matter of time before the second goal arrived but the visitors went closest just before the break when Ciaran Clark struck the crossbar with a header after a free kick and Anthony Stokes missed the rebound.
Stokes had two good chances after the interval, and James McCarthy shot over as the Irish improved drastically for the second half.
However, Kroos unlocked the visitors' resolute defense with a delightful ball for Schuerrle to turn and pick his spot.
Jerome Boateng struck the crossbar late on, but it was the Irish who made a late surge, before Kroos took advantage on a counterattack to send Ozil through to chip the goalkeeper.
