Actually the Revolution got most of its support from the deeply religious, socially conservative lower classes. As for how ir was successful the existing Shah's government was accused, more or less correctly, of being American stoogies
As for 'more dominant', this depends on who you are and what you believe. The old pro-American government was totalitarian, operated secret police, etc, just like the current one, it just wasn't theocratic. You'd hope you weren't a left wing student activist, for example, the secret police might have had some words for you.
If you're a good god fearing (Shia) Muslim, a large portion of the population, then you might actually have liked the new government better
The people who lost out big time with the Islamist government were women, honosexuals, and to an extent religious minorities, though Iran is no worse here than other Islamist governments in the ME like the Saudis
The revolution was quite popular. Khomeini's arrival to Tehran from exile in Paris, and later on his death, were occasions for some of the largest human gatherings in history. Iranians have massively improved their living standards since the 1979 Islamic Revolution and multiple polls show that they generally support the govt. Incidentally Women's literacy rates went from under 50% to 98%
http://iranprimer.usip.org/blog/2013/apr/01/un-stats-life-longer-and-healthier-iran
http://www.worldpublicopinion.org/pipa/articles/brmiddleeastnafricara/652.php
I think the most important thing to understand here is that at the start of the revolution it was anything but a foregone conclusion that it would be a) successful and b) resulting in a theocracy. The standard narrative in the scholarship on this revolution is that it would not have been possible had there not been a (temporary, fragile) coalition built between very wide sectors of the Iranian political spectrum. Communists, nationalists, Islamists, pretty much everyone was revolting against the Shah.
The second important thing when considering how the Islamic Republic became successful is to understand that the success of the revolution and the beginning of the Iran-Iraq War coincided. The fact that Iran was under attack from a Western-supported neighbor was a huge opportunity for the young, fragile Islamic regime to consolidate power, and forcefully implement its rhetorical strategies. It allowed Khomeini to position himself not just as a Muslim leader, but an anti-imperialist one as well. This is probably the most time-tested path to success in Middle Eastern politics -- if you can claim the anti-imperialist high ground credibly, it doesn't matter whether you're an arch-secularist (like Atatürk or Shah Reza Pahlavi) or an Islamist theocrat (like Khomeini), you will find enough support to consolidate power and maybe even fend off imperialist forces.