Dortmund outplayed their hosts throughout Saturday's clash at the Allianz Arena, with Klopp's decision to leave Bayern-bound top scorer Robert Lewandowski on the bench proving something of a masterstroke.
The high defensive line employed by Bayern boss Pep Guardiola was ruthlessly exposed by the pace and movement of Dortmund's attacking quartet of Henrikh Mkhitaryan, Marco Reus, Jonas Hofmann - all of whom scored - and Pierre-Emerick Aubameyang.
The result - Bayern's first home league defeat since October 2012 - restores Dortmund's three-point advantage over rivals Schalke in second place.
And Klopp was thrilled with his side's performance, as they responded perfectly after the disappointment of being knocked out of the UEFA Champions League by Real Madrid by laying down a marker ahead of a potential DFB-Pokal final against Bayern.
"If you beat Munich 3-0, you can really speak of a near-perfect game," said the 46-year-old, who was taking charge of his 200th Bundesliga game with Dortmund.
Klopp went on to hail the contribution of Mkhitaryan, who spurned numerous chances against Real but was clinical in opening the scoring on Saturday, and was buoyant ahead of Tuesday's Pokal semi-final clash with Wolfsburg.
"I think scoring will have done Mkhitaryan a lot of good - sometimes it's like he's carrying a heavy rucksack (after the disappointment of the Real game)," he added.
"We're now focusing on reaching the cup final. Once we're there, it doesn't matter who we play."
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