What brought their genuine panic to an end was a flurry of results, first from the Far East and then from Siberia and much of the rest of the huge nation that Mr Yeltsin so much yearns to govern for a second term.
One after another, they rolled in from the eastern seaboard the northern tundra, the Red Belt, the Urals. First, Primorsky, Sakhalin, Magadan, Khabarovsk - not particularly pro-government territory - put Mr Yeltsin ahead. And then, more predictably, Sverdlovsk, Chelyabinsk, St Petersburg, and elsewhere.
In Moscow, initial results gave the President 60 per cent of the vote, a result only bettered by the city's pro-Yeltsin mayor, Yuri Luzhkov, who was also running for re-election. Unofficial reports said Mr Luzhkov, whose running-mate was badly injured in a bomb attack earlier this month, had a 90 per cent lead in the city, which has benefited more than the rest of Russia from reforms.
However, the picture that was emerging last night, with 40 per cent of the votes counted, was one of a narrow two- to three-point lead for the President over the Communist Gennady Zyuganov. Although it is not a massive triumph, it will be enough to set him up well for a run-off in July. General Alexander Lebed was running a strong third with nearly 15 per cent, followed by the liberal economist, Grigory Yavlinsky, (8 per cent), and Vladimir Zhirinovsky (6.8 per cent).
Earlier in a nerve-wracking day, worried that Yeltsin's predicted support had failed to materialise, the President's advisers seemed to be deeply rattled. They drafted in several leading Russian artists who issued an extraordinary appeal to the electorate to go to the polling booths, only two hours before they closed in Moscow.
Their move came after initial figures showed that the turn-out was lower than the 75 per cent that Mr Yeltsin's team had hoped for, possibly because of the Russia-Germany football match. The development was seen as ominous for the President, whose record is marred by five difficult years of reform and a catastrophic war in Chechnya. In the event, the panic proved false; the turn-out was forecast at about 70 per cent.
Such was the concern within the Yeltsin camp that the Prime Minister, Viktor Chernomyrdin, a loyal supporter of the President, also publicly implored Russians to go to the polling booths "so as not to trade your future for an extra hour in front of television set or at your dachas [country homes] and vegetable plots."
His words were echoed by Sergei Solovyov, a film director, who made a blatant appeal to the public to vote for the president. He warned Russia's youth that they might "wake up in a different country" if they did not vote. In Moscow, the appeal either appeared to work, or was unnecessary; queues formed at polling stations which were so long that some voters were too late to cast their ballots.
But as the results unfolded, the Yeltsin camp relaxed. Mr Yeltsin's senior aide, Georgi Satarov announced that he was satisfied with the early results. "There is always maximum discomfort when you don't know what will happen," he explained.
That unease will also have been reduced by a CNN exit poll which placed Mr Yeltsin at 35 per cent, while Mr Zyuganov had 29 per cent. Despite fears of unrest, which heightened sharply when four people were killed by a bomb blast on Moscow's Metro system last week, voting went smoothly. There were several bomb scares around the country, but the only serious trouble occurred in Grozny, which saw its worst fighting in several weeks.
Earlier, Mr Yeltsin had struck a typically robust note as he voted with his wife, Naina. Asked if Mr Zyuganov could beat him, he cried "No way!", before telling reporters that he planned to spend the evening watching the football - a bizarre tactic, given that he needed Russians to do the exact opposite.
Like a boxer weighing in for the fight, Mr Zyuganov was equally full of rhetoric. "All the votes will be ours," he declared, as he voted in his Moscow district - a claim that was only slightly more improbable that that of the nationalist Vladimir Zhirinovsky, who announced he would get 27 per cent.
If the preliminary results are borne out, then Mr Yeltsin can go into the run-off feeling confident, not least because of the performance of General Lebed, with whom he is expected to forge an alliance. Even if the gap is narrower, and Mr Yeltsin and Mr Zyuganov finish neck-and-neck, then it will also be no disaster for the Kremlin.
To the relief of many in the West - who fear a return to Soviet-style controls - Mr Zyuganov stands little chance of expanding his core support sufficiently to beat Mr Yeltsin. If he was going to do so, he would have achieved it yesterday.
Early results from the polls
Preliminary official results of first round of the Russian presidential election with 29 million votes (around 40 per cent) counted.
Boris Yeltsin 34.35
Gennady Zyuganov 31.97
Alexander Lebed 14.71
Grigory Yavlinsky 8.16
Vladimir Zhirinovsky 6.86
Svyatoslav Fyodorov 1.02
Mikhail Gorbachev 0.57
Martin Shakkum 0.38
Yuri Vlasov 0.19
Vladimir Bryntsalov 0.16
(NOTE: total is less than 100 per cent because of votes against all candidates) Source: Reuters
Zyuganov on Yeltsin:
`One look at his face would tell you that democracy has never spent the night there'
Yeltsin on Zyuganov:
`He is for the destruction of everything that has been accomplished, under the banner of a socialist revenge'