Founding member Ralf Hütter, 68, collaborated with other artists to make 3D films to be projected in the signature glass-and-steel shell of the Neue Nationalgalerie (New National Gallery) while the quartet performed its trailblazing brand of "industrial folk music".
The stunning modernist temple by Bauhaus architect Mies van der Rohe is hosting the back-to-back shows before it closes for several years for renovation.
Kraftwerk's concerts have been sold out since November and come on the heels of other high-concept outings at the Sydney Opera House, New York's MoMA, the Tate Modern in London and Akasaka Blitz in Tokyo.
The Berlin dates mark the biggest spectacle staged by the band in the German capital in a decade.
Kraftwerk, founded in 1968, are credited with paving the way for acts ranging from Depeche Mode, New Order and Human League to Coldplay and Daft Punk.
'Little interest in being pop stars'
The notoriously reclusive band, based in the western city of Düsseldorf, has always shunned celebrity and even invented robot avatars to distance themselves from their on-stage personas.
"There's no pop band in the history of the music industry that has shown so little interest in being pop stars," Berlin's daily Morgenpost said.
The museum also opened in 1968, near where the Berlin Wall cleaved the city until a quarter-century ago.
It has since become a beloved cultural institution and tourist magnet.
Britain's David Chipperfield is managing the overhaul of the architectural landmark with the aim, he has said, of making the repairs imperceptible when they are completed.
Its collection of modern masterpieces by the likes of Pablo Picasso, Andy Warhol, Henry Moore and Gerhard Richter will be placed in storage or on loan in the meantime.
The museum said the Kraftwerk performances marked "a wonderful encounter between pioneers of the electronic age with a great visionary of public space".
Each night will showcase a different album, most made in the band's 1970s and 1980s heyday, followed by a greatest hits set.
Opaque black curtains covered the Neue Nationalgalerie's famous floor-to-ceiling front windows to keep the show an exclusive experience for 1,700 guests.
The four band members, dressed in skin-tight body suits accented with fluorescent grid patterns, stood at illuminated podiums, each equipped with a synthesiser.
Fans say the band has managed to stay cutting-edge.
"They were always ahead of their time with their modern sound and minimalist lyrics," said Claus Bölicke, 48, who works for a German charity.
"Their music is so catchy and the staging is so cool and very funny actually," said Friederike Schilbach, 34, who works in publishing and discovered Kraftwerk in the 1990s.
"I think sometimes people abroad got their humour more than Germans did."
'No warmth, no sex'
The enthusiastic, mostly middle-aged crowd cheered hits like "Das Model" and "Wir sind die Roboter" (We are the robots), which won the group an international cult following.
"Nearly all the new genres of pop music that developed in the following decades -- hip-hop, electro, Miami bass, house, techno, dubstep... were influenced by Kraftwerk," German weekly Zeit Magazin said recently.
More experimental art troupe than pop band, Kraftwerk, which means power station in German, picked up a Grammy lifetime achievement award last year.
Their lyrics about the growing dominance of technology in daily life and the omnipresence of machines are widely seen as prescient in a hyperconnected world.
Calling their musicians "audio operators", founders Hütter and Florian Schneider aimed to break with the pop music brought by the US and British occupying forces to create a new German sound.
"These unapproachable marionettes were the opposite of the blues – no warmth, no sex, no extroverted expressions. They were not the children of James Brown and Coca-Cola," news magazine Der Spiegel wrote this week.
Schneider announced he was leaving the band in 2008 and Hütter is the only original member remaining.
Music critic Kai Mueller said Kraftwerk's uber-German sensibility played to stereotypes that resonated abroad.
"Maybe they showed the world what we Germans were capable of: precision, excellence and yes, robot tears," he said.