The Moscow trial sparked protests around the world in support of the feminist activists, who have been called prisoners of conscience by international rights group.
Hundreds of their supporters chanted “Russia without Putin!” outside the courtroom, and several opposition leaders were detained.
The three were arrested in March after an unauthorised performance in Moscow’s main cathedral, high-kicking and dancing while singing a “punk prayer” pleading with the Virgin Mary to save Russia from Vladimir Putin, who was elected to a third new term as Russia’s president two weeks later.
Judge Marina Syrova said in her verdict the three women “committed hooliganism driven by religious hatred” and offended religious believers.
She rejected the women’s arguments that they were protesting at the Orthodox Church’s support for Mr Putin and did not want to hurt believers’ feelings.
Nadezhda Tolokonnikova, Maria Alekhina, and Yekaterina Samutsevich stood in a glass cage in the courtroom for three hours as the judge read the verdict. They smiled sadly at the testimony of prosecution witnesses accusing them of sacrilege and “devilish dances” in church.
The charges bear a maximum term of seven years in prison, although prosecutors requested a three-year term.
Mr Putin said the band members should not be judged too harshly, drawing expectations that they could be sentenced to time already and freed in the courtroom. Sceptics warned, however, that a mild sentence would look as if Putin was bowing to public pressure — something he has resented throughout his 12-year rule.
On the street outside, the courtroom, police rounded up a few dozen protesters, including former world chess champion Garry Kasparov, who is a leading opposition activist, and leftist opposition group leader Sergei Udaltsov.
Amnesty International said the ruling was a “bitter blow” for freedom of expression in Russia.
The case has has inflicted bruising damage to Russia’s reputation overseas and stoked the resentment of opposition partisans who have turned out in a series of massive rallies since last winter.
It also has underlined the influence of the Russian Orthodox Church. While church and state are formally separate, the church identifies itself as the heart of Russian national identity. Critics say its strength makes it a quasi-state entity.
The head of the church, Patriarch Kirill, has made no secret of his strong support for Mr Putin, even praising his presidential terms as “God’s miracle” and has described the performance as part of an assault by “enemy forces” on the church.
In weeks of protests around the world, celebrities including Paul McCartney and Madonna have called for the band members to be freed, and other protests timed to just before the verdict or soon afterward were held. In the Russian capital, activists put the band’s trademark balaclavas on several statues.
“I can’t believe that in the 21st century a judge in a secular court is talking about devilish movements. I can’t believe that a government official is quoting medieval church councils,” defence lawyer Nikolai Polozov said.
Before yesterday’s proceedings began, Mr Polozov said the women “hope for an acquittal but they are ready to continue to fight”.
The case comes in the wake of several recently passed laws cracking down on opposition, including one that raised the fine for taking part in an unauthorised demonstrations by 150 times to 300,000 roubles (about €7,200).
Meanwhile, a group of Russian activists have filed €8.5m lawsuits against Madonna and organisers of her Aug 9 St Petersburg concert, in which she reiterated her support for Pussy Riot and called for solidarity with gays and lesbians.
And Moscow’s top court has upheld a ban on gay pride marches in the city for the next 100 years.
Russian gay rights campaigner Nikolay Alexeyev had gone to court hoping to overturn the city council’s ban on gay parades.
He had asked for the right to stage such parades for the next 100 years.
He also opposes St Petersburg’s ban on spreading “homosexual propaganda”. The European Court of Human Rights has told Russia to pay him damages.
Yesterday Alexeyev said he would go back to the European Court in Strasbourg to push for a recognition that Moscow’s ban on gay pride marches was unjust.
The Moscow city government argued that the parade might cause public disorder.