There are many things to take into account about the Iranian Revolution of 1979 and background story about what happened in the previous years, but the thing is, there was an uprising and there was a popular movement that lead to the end of the Shah and the Tudeh party, the Iranian communist party, was a strong participant in the Iranian revolution.

As a background story, we have to consider the history of western exploitation and intervention in Persia and the CIA-backed coup against Mosaddegh. For decades, the Anglo-Persian Oil Company had been a matter of public humiliation among the Persian population. The company had a really generous concession on on Iranian petroleum since the beginning of the XX century and, like all the western petroleum companies that operated in the are, granted little benefits to the state they operated in, giving all the benefits to the imperial, western powers. For decades, the Iranian government had tried to negotiate a better deal regarding the Anglo-Persian Oil Company, at the time the biggest oil company in the world, but with little to no success. The story of the petroleum in Iran is connected to a series of humiliations in Iran. In 1941, during the Second World War, UK and Soviet Union occupied Iran and forced Reza Shah to abdicate in favor of the son, Mohammed Reza, in order to keep control on the petroleum resources during the Second World War and to avoid a German influence in Iran. Mohammed Reza was seen as a puppet of the west, doing even less than the father in trying to protect Iranian interests, and while the father pushed for reformation and westernization of Iran, the son was accused of having a complete rejection of Persian culture (symbolized by the completely western style palace he built), outlawing opposition (for example, the Tudeh party) and killing and torturing political opponents; finally, he was accused of being an extremely corrupt politician that squandered money. The situation got dramatically worse with Mosaddegh. Mosaddegh was a popular prime minister, initially democratically elected, that stayed in power from 1951 to 1953. He nationalized the Anglo-Persian Oil Company, first causing an embargo from the west of Persian oil, then the CIA organized a coup to reinstate the Shah into power. The image of Mosaddegh being arrested and humiliated, while the Shah came back to Tehran thanking the CIA, became an image of humiliation for the Iranian population, that fueled anger in the years to come.

Now what about Khomeini and the Iranian clergy? There are some characteristics that make the the Iranian, Shia clergy different than the Sunni establishment. First of all, the Sunni don’t really have a clergy class that is united and as organized as the Shia one. There are reasons for this, but I fear this comment will become too long. During the Pahlavi reign, the Shia clergy opposed modernization and westernization of the country, and while before it had been more apolitical, it started to develop a political theory, something completely new. Khomeini wasn’t the only one, but he surely was the most important, and with his theory of the Velayet-e-Faqih, that is the Guardianship of the Islamic Jurist, he believed that the Shia clergy has a role in granting that the state works according to Islamic laws and the opinion of Islamic jurists. There is more to that. There is, actually, some ideological influence from communism, in particular the political theory from Ali Shariati, a really interesting scholar that tried to put together the ideas of social justice, decolonization and class war with the traditional Shiism. He is considered one of the ideologues of the Iranian revolution.

In 1979, when the revolution started, it wasn’t only “Islamists” that started the revolution. Actually, there were a lot of student movements that participated and the Tudeh party (the communist party of Iran) was a really strong force behind it. Other oppositions participated, for example people close to the party to which Mosaddegh belonged. It was a huge, popular uprising that put together the religious supporters of Khomeini, the communists and left wing movements and all kind of other opposition. The problem is, as soon as Khomeini got to power, he dismantled all opposition, especially the Tudeh party, that was dismantled and its participant suppressed or exiled.

EDIT: Source for some of these information, Gli Sciiti by Anna Vanzan