They are part of a collection bought in the 1970s by dealers acting for Farah, the wife of Shah Mohammad Reza Pahlavi, who fled into exile in 1979, heralding Iran's Islamic revolution later that year.
Ever since the themes of many of the Western works have been considered too risque to be publicly shown and have spent much of the past 36 years languishing in storage in the basement of Tehran's Museum of Contemporary Art.
Among the 42 Western works featured in the museum's three-month exhibition is Pollock's "Mural on Indian Red Ground", completed in 1950 and considered one of his best drip paintings.
Five years ago, experts at Christie's said that, were it put on the market, it would fetch $250 million.
Also featured is Warhol's "Suicide", a 1963 acrylic of a man leaping to his death from a building. A similar work from Warhol's "Death and Disaster" series sold at Sotheby's in New York for $105 million in 2013.
The American artist Mark Rothko's "Sienna Orange and Black on Dark Brown" oil on canvas and Irish-born British painter Francis Bacon's "Reclining Man with Sculpture" are also on show.
They are part of a joint exhibition also featuring 130 works by famed Iranian artist Farideh Lashai. A painter, writer, translator and visual artist, she died in 2013.
Iran's Culture Minister Ali Jannati attended a preview on Friday night in a demonstration of official support from President Hassan Rouhani's government.
Jannati told AFP that the Islamic republic's recent nuclear deal with world powers had opened up potential for international cooperation in art as well as business and other fields.
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"This is a first step and we hope to have more mutual cooperation to showcase outstanding Iranian artists as well as displaying more works from our foreign art collection," he said.
The international works went underground after Iran's revolutionary leader Ayatollah Ruhollah Khomeini railed against "Westoxification", denouncing Western moral and sexual depravity which he said had infected the Islamic world.
Many films were banned from cinemas in Iran as was music and many books.
The Tehran museum did not hold a major exhibition of foreign art until 1999, a decade after Khomeini's death.
Iran was then under the reformist 1997-2005 government of president Mohammad Khatami.
The current exhibition was jointly curated by Iran's Faryar Javaherian and Italy's Germano Celant, who said he was astonished at the museum's collection.
"Many of them I had only seen before as reproductions but here we have the real thing," Celant said, noting that the basement held around 300 original pieces in storage.
Those include more than a dozen works by Warhol, including his Mao series of the Chinese communist leader, as well as Bacon's Triptych, part of which features two naked men lying on a bed.
When it was publicly shown in Tehran in 2005, it was quickly taken down, reportedly on orders from the ministry of culture and Islamic guidance. Jannati was not the minister at the time.
Celant, an art historian, critic and former senior curator at the Guggenheim Museum in New York, acknowledged that works such as nudes were out of bounds but said many others should not be.
More cultural exchanges could bring greater global prominence to Iranian artists such as Lashai, he said.
"For me, it's very important to start this kind of collaboration with Iran. This is a truly great international collection and it can help start a better connection between Iran and an outside audience."