The striker surpassed Gerd Muller's tally by netting his 69th international goal, but Joachim Low will no doubt be more concerned with the early withdrawal of one of his star men.
The Lazio forward came off the bench midway through the second half of the game in Mainz and headed home a Lukas Podolski cross in the 76th minute to take his international tally to 69, one ahead of the iconic Gerd Muller.
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However, of greater concern to coach Joachim Low will no doubt be the suspected ankle injury that forced Marco Reus off just before half-time that has put the Borussia Dortmund's World Cup hopes in doubt.
Germany subsequently took the lead through Andre Schurrle, but were pegged back by a penalty from Henrikh Mkhitaryan.
Armenia's equalizer came with 21 minutes remaining, yet the hosts subsequently pulled clear with further goals from Lukas Podolski, Benedikt Howedes and Klose before Mario Gotze rounded off the scoring with a late brace.
Germany can expect stiffer opposition in their World Cup opener against Portugal on June 16 but will surely take heart from the way it finished Friday's match at the Coface Arena in Mainz.
Armenia started brightly but almost fell behind when Hrayr Mkoyan cleared an effort from Reus off the line after the 25-year-old had been slid through by Thomas Muller.
Despite dictating play for much of the first half, Germany struggled to find a way through the Armenian defense.
Jerome Boateng headed wide from a corner before Reus was denied by a strong save from Roman Berezovsky.
The first ended then on a sour note for Low's men, as Reus was helped from the field in some pain following a tackle from Artur Yedigaryan.
Reus' replacement Podolski had a hand in Germany's opener as Schurrle found the net seven minutes into the second half.
Podolski broke free down the left-hand side, before teeing up Chelsea forward Schurrle with a pinpoint low cross.
Boateng lashed a fierce effort narrowly over the crossbar, and Mesut Ozil struck the post as Germany pushed for a second, but Armenia still carried a threat.
And the underdog drew level in the 69th minute when substitute Kevin Grosskreutz tripped Gevorg Ghazaryan in the area, allowing Dortmund teammate Mkhitaryan to coolly slot past another club colleague, Roman Weidenfeller, from the penalty spot.
Remarkably, Germany responded by firing in five goals in the final 18 minutes.
Podolski rifled a fine finish into the bottom corner from Ozil's neat pass, and Howedes swiftly made it 3-1 by converting a rebound after Berezovsky's brilliant inital save from his header.
Klose then grabbed his landmark 69th international goal with a diving header from another excellent cross from Podolski.
And there was still time for Gotze to capitalize on further slack defending with two late strikes.