The 24-year-old, who has been in top form for the Reds this season, opened his account by the 20th minute from the spot, moments after teammate Aleksandar Pesic opened the scoring.
Boakye made it 3-0 for his side after latching on to a pass from a teammate, before Aleksandar Lutovac pulled one back for the visitors four minutes to half-time
Pesic restored Zvezda's three-goal lead by the 54th minute before Boakye completed the riot with another brace within the last 27 minutes of the game.
Yiadom, who previously played for Juventus under current Chelsea manager Antonio Conte, has taken his tally to 22 goals in all competitions this season.
The Premier League defending champions are reportedly weighing up options to send a bid for his services in the January transfer window.