The 23-year-old scored his side’s third goal in the 73rd minute, before Andrey Solovery sealed the victory in the 82nd minute.
Igor Ivanovic and Sergey Politevich opened the scoring for Shakhyor earlier in the 39th and 67th minutes of the game.
Brikama-born player, Darboe has now scored his second league goal in two matches of the new Belarusian Premier League season.
The Gambian international now scored 21 goals in 28 matches since moving to the Budaŭnіk Stadium.
The victory moved FC Shakhtyor to 5th position with 4 points after two games.
Dembo signed for Belarusian side FC Shakhtyor after leaving Macedonian side Shkupi in January 2021, where he scored 18 goals in 41 games.