It followed a 3-0 penalty shootout victory over Aberdeen after a tense night in Gorgie as Craig Levein's men came from behind twice to take the game to extra time.
Having defeated Hibs 2-1 on Sunday there is a more positive feeling returning to the Hearts support.
The Tynecastle crowd was appreciative of the efforts of the players with Uche Ikpeazu getting a rousing applause for a sliding challenge late in the game, fans recognising the player continuing to work for the team despite being visibly shattered.
Yet, any fatigue seemed to disappear after Aidan Keena dispatched a penalty past Joe Lewis to confirm the win.
The Hearts players and substitutes ran to congratulate the Irish striker as well as Joel Pereira who stopped Bruce Anderson's penalty.
The most amusing aspect of the celebrations was Uche and Michael Smith. The big English striker was seen scampering towards Keena while carrying his team-mate on his back like a proud dad zipping about the back garden with his kid.
Ikpeazu was back to his chaotic best for Hearts as he led the line throughout the 120 minutes, causing panic amongst the Dons defence.