The primary reason why the Islamic Revolution became Islamic was that there was a lack of cohesion between the various groups you mentioned, from the paramilitary leftist organizations to ultra-conservative religious groups. Initially these groups only had one objective that tied them together, which was to overthrow Muhammad Reza Pahlavi. After the Shah fled to the U.S., this loosely tied revolution was thrown into disarray, and an inevitable power struggle would soon erupt.

First, the militant wing of the revolution—fundamentalists and leftists—purged the democratic forces. Then the Islamic revolutionaries went to war with the leftist revolutionaries. Finally, the conservative and pragmatist fundamentalist confronted the Radical and Left-leaning fundamentalists. What caused the Islamic revolutionaries to emerge victorious was that the other factions did not have either a coherent ideology or an ideology that had strong public support, or both.

For the democratic platform, its advocates lacked an ideology. Although they called for political reform, it was not the primary concern of the revolution. Inevitably in a social revolution, democracy falls victim to mass mobilization. For the ideologies of the Left, with various brands of communism and socialism, they had a solid plan to implement social and economic change. In the early part of the revolution, the Leftists successfully influenced policies, such as emphasizing the redistribution of wealth and confiscation of property from the rich. The problem was that the Leftist ideology ran against Ayatollah Ruhollah Khomeini and his followers, whom had their own concept of how a revolution should be ran. the general Marxist attitude toward religion as a reactionary force that has no place in a progressive society – and would be incapable of leading a revolution – blinded the Left to Khomeini’s power and potential. Thus, Khomeini was the only one capable of producing an Islamic ideology that could win the Revolution, while the Left fell victim to its blind spots of its own ideology.

For Khomeini to successfully convert his own religious and political agenda into the revolutionary movement, he would need to be a single Islamic ideology that could mobilize the masses and appeal to the revolutionary fervor. Indeed, Khomeini’s works prior to the revolution already established a basis for the masses to support. Khomeini defined Islamic ideology in terms of demanding an Islamic state that would bring about social justice, empowering the poor, and freeing Iran from Western political and cultural influence. This ideology was as much based on a fundamentalist view of Islam as it was on political and economic populism. In short, this had all the elements of Marxism, but Khomeini cleverly disguised it with religious symbol and language of Islam and led by the ulama. As a result, Khomeini was able to outmaneuver the Leftist by taking support away from those groups, crushing it and ending up controlling the revolution.

Sources:

Ali Gheissari and Seyyed Vali Reza Nasr, Democracy in Iran: History and the Quest for Liberty (Oxford: Oxford University Press, 2009).

Moaddel, Mansoor. Class, Politics, and Ideology in the Iranian Revolution. New York: Columbia University Press, 1994.