The agreement, arrived at in Geneva during the small hours with most foreign ministers of the P5 + 1 (the five permanent United Nations Security Council members, plus Germany) in attendance, ends a decade of tensions, uncertainty, and war talk over Iran's alleged nuclear ambitions.
Though it's only an interim accord, Mr. Lavrov said, it changes the whole perspective for solving other issues in the turbulent Middle East, particularly prospects for peace in civil-war-torn Syria.
The deal establishes Iran's right to enrich uranium for peaceful purposes, but imposes a freeze on nuclear construction and tough new standards of supervision over a greatly reduced program, in return for about $7 billion in immediate sanctions relief.
"Over the next six months, we'll be carrying out intensive talks to work out a final agreement along the lines that will allow Iran to continue" peaceful nuclear development and research, along with new tools for control by the International Atomic Energy Agency, Lavrov said.
"In the long run everybody will benefit from this, I think. First of all, we have settled the questions that many countries had about the Iranian nuclear program, and the risk that it could lead to weapons of mass destruction. Now it will be difficult [for Iran] to evade the new rules, and we can feel 100 percent positive that Iran will cooperate with the IAEA in a transparent way," he said.
Russia also believes "that this step brings us closer to the goal set by the global community in 2010 to organize a conference dedicated to creating a nuclear weapons-free zone in the Middle East," he added.
Lavrov praised President Hassan Rouhan, Iran's new president, for bringing a fresh spirit of compromise to the problem, and complimented the leaders of P5 + 1 nations for their ability to hold a unified position and see the deal through to success. He added that the agreement vindicates Russia's long-held insistence on finding a negotiated solution along exactly such lines.
"This is a call to strengthen trust and allow our partners from the US and EU to relax the pressure of sanctions that they brought in against Iran, introduced unilaterally, without a decision of the Security Council. We have never recognized these sanctions and it’s probably right to get rid of these unilateral sanctions in order to relax this strain on Iran," Lavrov added.
Experts with state-supported think tanks agree that Russia's role as a country straddling the East-West geopolitical divide was pivotal.
"Lavrov has argued all along that the problem should be tackled step by step," says Vladimir Sazhin, a Middle East expert with the official Institute of Oriental Studies in Moscow.
"Everybody knew the problem was big, and had to be solved, but the Russian position gave it a direction. This is not just a technical point, Russia's role was morally important, too. At some of the toughest moments in the talks, when everyone was losing heart, Russian negotiators came up with new approaches and injected hope into the atmosphere," he says.
Georgi Mirski, an expert with the official Institute of World Economy and International Relations in Moscow, says that with war clouds receding, the door is open for new trade and investment opportunities in Iran.
Though Russia joined the West in imposing some Security Council-approved sanctions on Iran, Moscow has not signed on to the majority of Western sanctions. Russian companies have thus maintained many positions in Iran that may give them a head start if peace brings a fresh commercial boom.
But it's not exactly correct to say there are no losers in the deal, Mr. Mirski says.
"It's a black day for [Israeli Prime Minister Benjamin] Netanyahu. I was at a meeting with him [when he visited Moscow] three days ago, and he made it very clear that he views any such deal as bad. He thinks the West is stepping into a trap.
"But one thing is clear: there will be no war in the near future. Israel is very unlikely to strike Iran on its own. So the world has got a breathing space, and we can live without fear for some time at least."