The cut off time had been pushed back eight hours to 6pm (15:00 GMT) to allow Yushchenko time to meet Putin.
Russia, which has a record of gas rows with Kiev, is not keen to alienate a neighbour torn between integrating with Europe and keeping traditionally close ties with Russia.
"Ukraine is a great neighbouring state with which we should build friendly, open and sincere ties rather than neutral relations like with Poland for instance," local news agencies quoted Sergei Prikhodko, Putin's foreign policy adviser, as saying.
Gazprom has said that it would only cut Russian-origin gas and that its contracts with customers further downstream would be fulfiled.
A repeat of supply disruptions to Europe would renew Western concern about Russia's reliability as an energy partner, even as it undertakes massive new projects to sell gas to Europe.
European supplies were affected in 2006 during a price dispute between Kiev and Moscow which was seen as rooted in Russia's unhappiness that Yushchenko, seen as pro-Western, had come to power a year earlier.
Moscow has recently been angered by Ukraine's renewed drive to seek membership of Nato and the EU in a step to move away from Russia's sphere of influence.