Rudy fired a remarkable outswinging shot from long-range past Michael McGovern after two minutes and Wagner scored with another emphatic effort in the 21st as the world champions clocked up their ninth successive win to move on to 27 points.
Joshua Kimmich added a third in the 86th minute as the hosts' run of five successive wins was brought to an abrupt halt. Josh Maggenis scored a consolation in stoppage-time.
Northern Ireland have 19 points from nine games and had already made sure of a two-top finish before the match. However, they are still not certain of finishing as one of the eight best runners-up up in the nine European groups.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The group winners qualify directly for Russia along with four winners of the playoffs which involve the eight best runners-up.
"I'm satisfied. We scored and early goal and then controlled the game, like we wanted to," said Germany coach Joachim Loew, whose side have scored 38 goals and conceded three in qualifying.
Northern Ireland had won their first four home games in the group without conceding a goal but that record was quickly ended by Rudy's thumping effort.
The hosts, backed by a boisterous crowd, were repeatedly exposed and McGovern made a superb save at point-blank range to keep out a Sandro Wagner header three minutes later.
Wagner headed against the post from Kimmich's pinpoint cross before being rewarded with Germany's second goal, collecting Thomas Mueller's pass with his back to goal before turning and firing a left-foot shot past a shell-shocked McGovern.
Germany goalkeeper Marc-Andre ter Stegen was tested once in the first half when he dived at the feet of Corry Evans after he got free in the area.
"This was a bonus game for us, it could have gone to 4-0 or 5-0 but we kept out goal difference in a healthy state," said Northern Ireland coach Michael O'Neill. "It could easily have been obliterated."
The hosts put Germany under more pressure in the second half and the best chance fellow to Conor Washington who clipped the bar from an excellent position.
Kimmich fired the third for Germany, although they were denied a clean sheet Maggenis's goal, which left the home crowd celebrating as if their team had won.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
