The Phobians were looking to end their 2021/2022 season on a bright note after finishing 6th in the Ghana Premier League.
Emmanuel Avornyo scored for Bechem United the lead in the 45th minute but fantastic goals from midfielder Caleb Amankwah and striker Daniel Afriyie Barnieh won the day for the glorious club founded in 1911.
For Hearts coach Samuel Boadu, it was his second FA Cup in succession after leading Hearts to victory in the 2020/2021 season.
Hearts of Oak will take part in the CAF Confederation Cup qualifiers.