Nadezhda Tolokonnikova, 22, Maria Alyokhina, 24, and Yekaterina Samutsevich, 30, were convicted of hooliganism motivated by religious hatred over their performance of a "punk prayer" urging the Virgin Mary to rid Russia of Putin.
The three wore masks to conceal their identity but were arrested after the protest. Two others who took part remain at large and the group has said it plans further demonstrations against Putin.
In an interview last week, other members of Pussy Riot, their faces hidden behind colorful ski masks, said the trial had only strengthened their resolve.
The European Union and a number of countries have called the sentences disproportionate, and the United States has urged the Russian authorities to review the case.
Tolokonnikova, Alyokhina and Samutsevich said they had sought to protest against Putin's close ties with the Russian Orthodox church and had not set out to offend believers.
Putin, who returned to the presidency for a third term on May 7 after a four-year spell as prime minister, said before the sentencing that the women did "nothing good" but should not be judged too harshly.
They have already been in jail for about five months, meaning they will serve another 19, and could be freed if Putin were to pardon them. The Orthodox church hinted it would not oppose such a move by appealing, belatedly, for mercy.
Intellpuke: You can read this Reuters article, filed from Moscow, Russia, in context here: www.guardian.co.uk/music/2012/aug/20/russian-police-hunt-pussy-riot