Rudy and Wagner's glorious first-half strikes had their place all but wrapped up before Kimmich scored late on to extend Germany's remarkable unbeaten away record to 47 World Cup qualifiers dating back to 1934.
"We're off to Russia, to tear it up! We want to successfully defend the World Cup title," said Rudy.
Germany coach Joachim Loew said: "I'm happy. We knew the Northern Irish would play very defensively and they know how to do that well. But we began well and we let them have very few chances."
The Northern Irish, for whom Josh Magennis grabbed a late consolation, couldn't give manager Michael O'Neill a memorable scalp on his 50th match in charge as they slid to their first competitive home defeat since Portugal beat them 4-2 in September 2013.
However, they can still look forward to a place in the play-offs and a possible trip to Russia.
"This was a bonus game for us, it could have gone to 4-0 or 5-0 but we kept our goal difference in a healthy state. It could easily have been obliterated," said a relieved O'Neill.
Rudy first for country
The raucous 18,000 crowd were silenced within two minutes as Rudy lashed home a stunning right-footed effort into the top corner from outside the area that gave Michael McGovern no chance.
It was 27-year-old Rudy's first goal for his country in his 22nd appearance and brought to an end the hosts' hope of equalling the record for successive clean sheets of six set by the side who qualified for the 1986 World Cup - the last time Northern Ireland reached the global showpiece.
McGovern though kept his team in the match a few minutes later as he pulled off a stunning reflex save to deny Wagner.
The visitors dominated the hosts, with only the post saving the Northern Irish saved from going further behind from Wagner's header.
However, the irrepressible Wagner would not be denied a third time, the 29-year-old Hoffenheim striker's sublime curling left-footed strike in the 20th minute flashing past McGovern for his fourth goal of the campaign.
The hosts were living off scraps and rarely able to get out of their half but they were presented with a glorious chance to reduce the deficit five minutes before half-time.
A great ball in from the right by Magennis fell to Corry Evans who was fortunate to get a second chance after a poor first touch but could only poke an effort which took a deflection off Marc Andre ter Stegen for a corner.
The hosts - for whom Michael O'Neill sent on Stuart Dallas and Conor Washington to add more vim going forward - were grateful to McGovern again as he produced another top-class save to deny Thomas Mueller in the 50th minute.
Northern Ireland should have made it 2-1 with 15 minutes remaining after the industrious Magennis got the better of Mats Hummels and set up Washington whose rising effort struck the crossbar.
The visitors got a third four minutes from time as the unmarked Kimmich scored, his shot beating McGovern at the near post.