Suddenly a world which worries about an unpredictable nuclear state has been taken aback by a new kind of power.
Now it's Iran's "charm offensive" that's causing a stir.
A country whose image is often portrayed in black veils and clenched fists now has a smiling, twinkly-eyed, tweeting president reaching out to the West.
When news broke on Friday of a historic telephone call in New York between an American and an Iranian president, social media fizzed with excitement and euphoria.
"Given how painless that was, and how many millions of people it made happy, it's amazing it took 34 years to make that call," remarked leading Iran expert Karim Sadjadpour of the Carnegie Endowment for International Peace.
Biggest tabooOne of the most extraordinary tweets from the @HassanRouhani twitter account was: "In a phone conversation b/w #Iranian & #US Presidents just now: @hassanRouhani: "Have a Nice Day!"
@BarackObama: "Thank you. Khodahafez [Goodbye]."
The return to Tehran descended into a chaotic reminder of Iran's fractious politics”
End QuoteAfter three decades of talking past each other, the Iranian and American leaders seemed to be speaking the same language, at least for some of the words it takes to fill 140 characters on Twitter.
"The biggest taboo in Iranian politics has been broken," remarked Ali Vaez of the International Crisis Group.
While on his trip to New York during the United Nations General Assembly, President Rouhani even dropped one of the defining anti-American slogans of the Islamic Revolution. He referred to the United States as "the great nation", rather than "the Great Satan."
But like a late-night celebration which loses its sparkle in the bright light of day, so did a tantalising buzz lose some of its allure.
By the time the Iranian president and his entourage landed in Tehran, the stream of tweets describing his 15-minute conversation with President Obama had been removed from his account.
And after a New York visit which seemed carefully choreographed, the return to Tehran descended into a chaotic reminder of Iran's fractious politics.
"He returned to reality on the ground," observed my Iranian colleague Amir Paivar watching developments from London.
A reality check came from both sides of a political divide often defined by attitudes to opening up to the West. "Long live Rouhani, everlasting change," chanted one group while cries of "Death to America" rose loudly from another.
Even eggs and shoes were hurled.
Thomas Erdbrink of the New York Times, one of the few Western journalists in Tehran, reported that "President Rouhani was trying to keep smiling but security people tried to shield him off with an umbrella, then pulled him into car and drove off."
Political protection was provided by the official who received him - Dr Ali Akbar Velayati, representative of Iran's most powerful player, the spiritual leader Ayatollah Ali Khamenei. It sent a signal that the elected President Rouhani is the Ayatollah's man, empowered by him to achieve results, especially when it comes to easing the sanctions crippling Iran's economy.
"The excitement is outside, we still don't feel it here," a leading businessman in Tehran told me by telephone. "Nothing has happened yet when it comes to sanctions."
BeamingStill, social media in Iran was awash with the cautious hopes of those in a young generation with access to the internet, who are chafing at a life of rules and restrictions.
In the past one side was ready and the other was not”
End QuoteTrita ParsiOptimism of some kind was also evident in a tweet which wasn't removed from President Rouhani's account. A photograph showed the 64-year-old cleric beaming just after he finished his momentous telephone call and boarded the plane to take him home.
"President Rouhani is a pragmatic politican," explained Ali Vaez. "He had the courage to cultivate this historic moment for thawing relations with the US whilst having the prudence to do it in a way that would reduce risks for a domestic backlash."
Informed observers believe Ayatalloh Khamanei, known to be deeply suspicious of the West's intentions, has given the reformist president a window to show results.
That may explain why President Rouhani spoke, with surprising optimism, of a nuclear deal within three to six months.
Much will depend on how the international community responds to this outreach.
"In the past one side was ready and the other was not," commented Trita Parsi in a nod to years of missed opportunities for some kind of engagement.
"Now two sides are moving at the same time," said Parsi who heads the US-based National Iranian American Council.
President Obama has made clear that "while there will surely be important obstacles to moving forward and success is by no means guaranteed, I believe we can reach a comprehensive solution".
In New York, President Rouhani reiterated his country's key demand in years of protracted nuclear talks . "We will never forego our inherent right to benefit from peaceful nuclear technology, including enrichment."
But he also emphasised Iran would "leave no stone unturned" to reassure the world that its nuclear programme was entirely peaceful.
There's still some scepticism and cynicism over this new-look Iran. The loudest warning came from Israel's Prime Minister Benjamin Netanyahu who's described the Iranian president as "a wolf in sheep's clothing".
A change in tone will soon be put to the test in the next round of talks between Iran and world powers set to take place in Geneva in mid-October.
The first encounter in New York, where Iran's American-educated Foreign Minister Javad Zarif opened the meeting and sat next to the US Secretary of State John Kerry sent an even more substantial message of change than the presidential call.
In the end, it will come down to what will be many months of old fashioned face-to-face talks between two countries, with a history of enmity and fundamentally different world views, which now realise there are good reasons to engage.
There are also certain to be many more mundane telephone calls and, perhaps, a more restrained succession of tweets.
Suddenly a world which worries about an unpredictable nuclear state has been taken aback by a new kind of power.