The forward struck in the first half to secure the three points for Joachim Low's men and ensure they finish ahead of Poland in Group C, while Michael O'Neill's side finish third.
Mario Gomez's goal wrapped up top spot for Germany in Group C as a 1-0 win at the Parc des Princes left Northern Ireland waiting to find out their own fate at Euro 2016.
Having failed to impress in a bore draw against Poland last time out, Joachim Low's side again struggled to hit top gear despite dominating against one of the tournament's biggest underdogs in Paris.
Michael O'Neill's plan to stifle the world champions always looked likely to fail, with goalkeeper Michael McGovern – who was impressive throughout – called into action several times before his defences were breached.
Gomez marked his first start in France with a close-range 29th-minute finish, while Thomas Muller hit the post and crossbar among a host of other Germany chances before the interval.
Though Northern Ireland now needed a goal to claim the point they clearly came for, it proved close to impossible for them to relieve the constant pressure.
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