While the area that is modern day Iran was indeed never colonized the way that India was, the country was picked apart bit by bit in the 1800s and what was left was more or less defacto colonized by Russia and Great Britain. Although there were resources to be had, nothing was quite so valuable as to engage a Great Power in a series of costly and strategically risky colonization efforts.

As a starting point, a huge area of the middle east, centered in Persia, was controlled by the Safavid Empire through much of the early modern era. Similar to the Ottomans or the Mughals, they had a strong government, a standing army made of slaves similar to the effective Ottoman Janissary system, and in the later years a modern gunpowder based musketeer force.

During the early to mid 1700s, Persia was on a decline. Indian silk was booming in Europe (and drawing some uncomfortable looks from colonizing powers), causing disruption to the economy. Huge swaths of Safavid territory were lost to the Ottomans and to Russia, in a series of wars launched by Peter the Great. A brief resurgence in the mid century would actually see the territory reconquered, but the country subsequently declined again after their ruler was assassinated, their economic woes continued, and the Safavid dynasty ended. By the turn of the century, as the colonizing powers strengthened their hold on India and the East, what would become modern day Iran was much diminished compared to it's past Imperial self.

The 1800s weren't all that great for Iranian empires either. More wars with the Russians would lose them most of the Caucasus, Amernia, and some northern cities. A series of wars with Great Britain would lose Herat and eastern territories which were heavily populated and filled with useful agricultural products like saffron. At this point Iran could more or less see the writing on the wall.

In response to Iran's growing losses and the obvious influence of Britain and Russia, the new Qajar Dynasty ended up more or less acting as puppets to the great powers. Colonization was costly and intensive, and intervention by any power in Iran could have drawn a response from one of the other powers. With this knowledge, and with new diplomatic ties to the west, successive Qajar monarchs sought to modernize Iran, and play western powers off each other, to varying degrees of success. Iran would remain nominally independent, but more or less entirely existing because it lay in both Russian and British spheres of influence. Neither Power willing to commit to an invasion, but both with significant influence in the region.

Iran's situation was precarious, but hadn't changed for generations of Qajar rulers. Just to make things interesting, as the world rapidly approached the end of "classical" colonization coming after World War II, oil was found in the Middle East in the early 1900s (again drawing those uncomfortable looks from hungry Western powers). Almost concurrently, several terrible famines struck the region and millions of Iranians died. The hundred years of more or less "stable" rule quickly crumbled in a rapid-fire series of events.

Iran found itself under (mostly neutral) occupation by British, Russian and Ottoman forces during WWI. The Russians suffered their own revolution, the Ottomans collapsed, and the British unsuccessfully tried to setup a protectorate. The resultant interwar years were filled with several internal revolutions and coups, a brief constitutional monarchy, a military dictatorship, but ultimately independent, Iranian rule. After several hundred years of conflict with western powers, Iran was finally occupied in WWII by a joint invasion of the Soviet Union and Great Britain. I do find it somewhat telling that the only time an occupation like this happened was with the agreement of both British and Russian forces.

However, this wasn't an occupation with the intent to colonize. Iran had just made it just under the bar for that particular form of control. Instead, Iran got to be the very first theater in a different kind of geopolitical power game, the Cold War. The resultant Iran Crisis of 1946 over the withdrawal of the Soviet forces would end up with the eventual relinquishing of Soviet control in the area, and (with some words from the USA) the Iranians would even get to keep their oil.

I would tend to frame what happened to Iran, not as "avoiding" colonization, but merely getting by until colonization wasn't the preferred method for influence in a country. Iran suffered a CIA lead Coup in 1953. To this day, even after the Revolution of 1979, Iran continues to walk a line between spheres of power. It's not "free" from them, no country is really, but it maintains independence by being costly to invade, and being willing to push and pull a little to play the major powers off each other. I don't find it hard to think of some topical examples where this continues right into modern day.