Judge Marina Syrova convicted the women of hooliganism motivated by religious hatred, saying they had "crudely undermined social order".
The women say the protest, in February, was directed at the Russian Orthodox Church leader's support for Mr Putin.
The closely watched trial has inflamed opinion both at home and abroad.
Prosecutors had been seeking a three-year jail sentence for the women.
Judge Syrova said Maria Alyokhina, 24, Nadezhda Tolokonnikova, 22, and Yekaterina Samutsevich, 29, had offended the feelings of Orthodox believers and shown a "complete lack of respect".
"Tolokonnikova, Alyokhina and Samutsevich committed hooliganism - in other words, a grave violation of public order," she said.
The judge quoted prosecution witnesses as saying the act had been one of blasphemy, not politics.
Along with other members of their band, the women staged a flashmob-style performance of their song close to the altar in the cathedral on 21 February.
Their brief, obscenity-laced performance, which implored the Virgin Mary to "throw Putin out", enraged the Orthodox Church - its leader Patriarch Kirill said it amounted to blasphemy.
Mr Putin was elected for a third term as president two weeks later.
Alyokhina, Tolokonnikova and Samutsevich, watching Friday's proceedings from inside a glass-walled cage in the courtroom, smiled as the widely predicted conviction was announced.
The judge then took three hours to read the verdict, before handing down "two years deprivation of liberty in a penal colony" for each defendant.
One man in the courtroom shouted "shame" at the sentencing, and there were chants and whistles from the band's supporters outside.
Tolokonnikova's husband, Pyotr Verzilov, said: "Russia's image was quite scary even before [this]. What happened now is a clear sign that Russia is moving towards becoming more like China or North Korea."
Opposition leader Alexei Navalny added: "They are in jail because it is Putin's personal revenge. This verdict was written by Vladimir Putin".
On Thursday, Tolokonnikova had said she was "not bitter about being in jail". But, speaking through her lawyer on Twitter, she said: "Politically, I am furious."
Ex-world chess champion Garry Kasparov was among several people arrested outside the court in Moscow
"Our imprisonment serves as a clear and unambiguous sign that freedom is being taken away from the entire country," she said.
The women have been detained for the past five months.
Associated Press news agency said a number of protesters had been arrested outside the court before the sentencing was announced, including ex-world chess champion Garry Kasparov and opposition politician Sergei Udaltsov.
There were also pro-Pussy Riot protests in Paris, where demonstrators in Igor Stravinsky square chanted "Freedom", and in Kiev, where women protesters sawed down a wooden cross in a central square.
Other shows of support took place in Belgrade, Berlin, Sofia, London, Dublin and Barcelona.
The band have also had vocal support from artists including Paul McCartney and Madonna, and from politicians.
Critics of the band have also been demonstrating, saying the stunt was an insult to the Russian Orthodox Church.
One, Igor Kim, told the BBC News website from Moscow: "Shouting and screaming and spreading hate in Church is unacceptable and is contrary with Christian ethics."
One protester outside court in Moscow simply shouted: "Let Pussy Riot and all their supporters burn in hell."
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