Hearts moved into the Scottish Premiership's top six after beating Ross County to dent the visitors' own hopes of finishing in the upper half of the division.
Elton Kabangu scored the opener midway through the first half, with substitute Jorge Grant sealing the victory in the final minute.
After a fairly dull start to the game where neither team were able to make an impact, Hearts eventually made the breakthrough.
Beni Baningime, who was pulling the strings in midfield, won the ball 25 yards from goal and slipped a pass into the path of Kabangu.
The striker was being closed down and, while he failed to connect cleanly with the ball, it was enough to sneak past goalkeeper Jordan Amissah.
The goal gave Hearts a boost and when Lawrence Shankland slid the ball into the path of teenager James Wilson, a second goal looked likely. But the 18-year-old Scotland squad member had his right-footed effort saved.
The visitors were restricted to counter-attacks, with Kieran Phillips allowed an effort on one such occasion, but the ball was deflected wide.
With just over an hour gone, County introduced strikers Jordan White and Ronan Hale in an effort to find the key to open the home defence.
Hearts responded by bringing on Grant and Calum Nieuwenhof.
And the home side doubled their advantage - and sealed the win - when Musa Drammah got the better of Eli Campbell down the right and slid the ball into the path of Grant, who slid home.