Kenneth Okoro scored the only goal of the match in the 24th minute to give Hearts all the valuable points at stake.
The win was the Phobians’ second successive win in their quest to avoid the drop and it has moved them 4 places up to eleventh on the league table.
Bechem United, however, have now dropped into the relegation zone and are occupying the 15th position.
In another Match day 27 game played at the Sunyani Coronation Park, bottom-placed BA United drew 1-1 with New Edubiase.
Bismark Idan scored the opener for Edubiase before Samuel Norgbey got the equalizer to see the two sides earn a point each from the game.