Joshua Kimmerich added the gloss four minutes from time before the hosts salvaged some pride with a stoppage time consolation goal from Josh Magennis.
It was Germany's ninth consecutive win in Group C. Despite the defeat Northern Ireland remain second in the group and in line to qualify for next month's play-offs for a berth in next summer's football fest.
"We're off to Russia, to tear it up! We want to successfully defend the World Cup title," said Bayern Munich midfielder Rudy following his first international goal.
Germany beat Argentina 1-0 at the Maracana in Rio de Janiero to claim the 2014 World Cup. While the Germans have been imperious during their qualifying camapign, Argentina have struggled in the South American qualifying zone.
On Thursday night, Argentina drew 0-0 with Peru to leave them sixth - one place off the spot for a play-off.
Argentina have one last chance for automatic qualification. On 11 October they play in Ecuador and a victory there - coupled with slip ups for Chile, Colombia or Peru would allow them into one of the top four places. Argentina's arch rivals Brazil have already booked their ticket for Russia and will go to the tournament as winners of the South American qualifying zone.