Joachim Low's men took a giant step toward securing their ticket to Brazil after Sami Khedira's 11th-minute strike had given the hosts a slender half-time lead, as Andre Schurrle and Mesut Ozil sealed their nation's progression in the second half.
Interim boss Noel King took charge of the Boys in Green for the first fixture in the post-Giovanni Trapattoni era, and the 57-year-old nearly saw his men take a surprise lead.
The Celtic man would soon regret his decision, as the Germans opened the scoring minutes later through Khedira, whose effort from outside the box took a wicked deflection off the boot of Ciaran Clark and wrong-footed goalkeeper David Forde.
King will be thanking Forde for keeping the deficit to a minimum, as the Millwall shot-stopper was later forced into two impressive saves; first denying a Schurrle header from point-blank range, before tipping Thomas Muller's long-range effort over the bar.
Despite their dominance, Germany nearly surrendered their advantage right on the stroke of half time, as Clark's looping header bounced off the woodwork, before Stokes produced an air-kick in attempting to convert the rebound.
Buoyed by their near miss, the Irish emerged from the interval as the stronger team and could have levelled matters directly from the restart, but Stokes dragged his long-range effort wide of the Manuel Neuer's post.
Soon it was two, though, as Schurrle beat the offside trap and nonchalantly controlling Muller's lofted pass, before swivelling and firing past Forde.
The Irish refused to bow out with a whimper and continued to create enough opportunities at the other end to test Neuer, as Stokes once again came close to halving the deficit but the Bayern Munich stopper did well to narrow the angle and parried away for a corner.
Jerome Boateng saw an effort to kill off the contest cannon off the post, before Ozil put the result beyond doubt, clipping over Forde to ensure Germany join the likes of Italy, Belgium and the Netherlands as Europe's only representation in the World Cup thus far.