As old UN hands recall, Stevenson aggressively sought a response from Zorin over allegations of Soviet nuclear missiles stationed in Cuba.
"Yes or no?" Stevenson demanded, and added the punch line: "And don't wait for the translation," as he pressed for an immediate answer from the Russian-speaking envoy.
Zorin turned to Stevenson and said, through a translator: "I am not in an American court of law, and I do not wish to answer the question put to me in the manner of a prosecuting counsel."
Stevenson famously responded that he would wait for an answer "until hell freezes over".
Judging by the recent deadlock in the Security Council over Kosovo, Iran, Burma, Zimbabwe, Sudan and most recently Georgia, one wonders whether the days of the Cold War are back, or at least its political rhetoric.
In January last year, a Western-backed and U.S.-led move to castigate the Burmese government for human rights violations suffered a rare double veto from China and Russia. Last month, history repeated itself when the two vetoed a resolution aimed at imposing sanctions against Zimbabwe.
The US-Russian political confrontation in the Security Council has intensified in recent weeks with the Russian invasion of Georgia, and Moscow's subsequent decision to recognise the breakaway territories of Abkhazia and South Ossetia.
When US Ambassador Zalmay Khalilzad sought a response from Russian Ambassador Vitaly Churkin on whether or not the Russians were bent on violating the territorial integrity and sovereignty of Georgia, Churkin said he had already provided an answer to the question.
Maybe, he added sarcastically, the US representative had not been listening when Churkin had given his response. "Perhaps he had not had his earpiece on," he added.
And when US Ambassador Alejandro Wolff recently blasted Russia for its perceived violations of international law and the UN charter during the invasion of Georgia, Churkin hit back with another dose of sarcasm.
"Did you find any weapons of mass destruction in Iraq...and are you still looking for them?" he asked.
Speeches laced with sarcasm and personal insults are rare in the Council chamber. But the Cold War rhetoric is back.
"The United Nations is not headed for a new Cold War," predicts Phyllis Bennis, director of the New Internationalist Project at the Washington-based Institute for Policy Studies. As US economic, political and diplomatic power diminishes around the world, military power has become ever more dominant as a viable tool of hegemony.
Partly as a result of that rising militarism and partly out of longstanding habit, she pointed out, governments around the world continue to treat the United States as if it were still an unchallengeable dominion.
"And in the United Nations, that means allowing Washington to continue to call the shots," added Bennis.
Just after the Cold War, Washington was in less of an ideological mode. Maybe it felt it could afford to be magnanimous without behaving in an overbearing and unilateral manner. But in the last eight years diplomats say the Americans have become increasingly ideological and unilateral.
One Asian envoy said the ideological zeal of the United States is also seen in the tendency by the West to try to broaden the definition of what is a threat to international peace and security. In Zimbabwe and Burma, democracy, elections, and human rights all fell under possible new definitions of 'threats'.
Russia and China are becoming more assertive, primarily on issues that bear directly on their own national interests, like preventing the Security Council from producing a resolution on Georgia.
Diplomats here don't see either side backing off for the time being. The West will continue to push the envelope and many among the Rest will continue to resist.