Hearts boss John McGlynn thanked fans for the support they have shown the club during a financial crisis but warned: "We are not out of the woods yet."
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The Jambos initially thought Saturday's Clydesdale Bank Premier League clash with St Mirren could be the last game in their 138-year history after being issued with a winding up order 11 days ago.
Club bosses have since reached agreement with Her Majesty's Revenue and Customs to extend the deadline for payment of a £450,000 tax bill until December 3.
There was further good news ahead of the 1-0 win over Saints at Tynecastle when Hearts announced that fans have raised more than £500,000 so far through a share issue launched last month.
McGlynn is relieved that Hearts appear to have staved off the immediate threat to their existence but admits there is a long way to go before they can resolve their financial problems.
He said: "We've got to put a brave face on things and show a good front but you are worried.
"It is great that £500,000 has been raised and it looks as though we are going to get past that one.
"But we need everyone to continue to back us.
"We can't thank the people enough who put their hands in their pockets and bought the shares but there is still a long way to go.
"If anyone else can get the money together, then we want them to do that because we are not out of the woods yet."
Danny Grainger grabbed the only goal of the game in front of a sold-out home crowd of 16,443 and McGlynn felt it was important to repay the fans by providing a positive result on the park.
He said: "There was a massive Hearts support here today.
"We can't thank the fans enough for their support, not only coming along but for the £500,000 in shares and the money the club has taken in.
"We wanted to give them a victory and we managed to achieve that.
"From our point of view, everyone Hearts-minded has gone out of the ground very happy.
"We can't do a lot off the pitch. We can go to some of the fundraising events and we can do bits and pieces, as the players have done this week.
"But the main place we can do it is on the pitch, that's where we can do our part and I felt that we did that today."
The result left Saints with six SPL defeats in a row and just a single point ahead of bottom side Dundee.
Buddies boss Danny Lennon said: "It was always going to be a difficult venue for us to come to today with the current situation at Hearts and them looking to survive.
"Coming into a wonderful arena and a packed house and a hostile environment, we knew it was going to be a challenge.
"I thought we handled it well, and handled Hearts well, but a deflected goal was the difference between the sides."