The Scottish Cup holders owe £450,000 in unpaid tax and were initially given until Friday to pay up or face a winding-up order from Her Majesty's Revenue and Customs.
But a new deal with HMRC means Hearts can pay the money in two instalments, the second of which is due in the first week of next month.
A series of supporter-led fund-raising initiatives have been supplemented by the decisions of several high-earning players to defer their wages.
And Hearts director Sergejus Fedotovas said: "We are pleased we have been granted this extension as it acknowledges the strenuous efforts that are going on to ensure this club continues to contribute to employment, society, community and football in Scotland.
"I also want to acknowledge the support received from political and supporter groups. Their direct action is helping the club through a very important period.
"We have a lot of hard work ahead of us in order to fully rectify our financial position but with further backing and ongoing fundraising by supporters we know that we have a very positive opportunity to create a strong club for the future.
"The supporters' efforts have been quite phenomenal. However, it is essential that they continue all their work to assist us in meeting financial targets at the club."