The Dockers knew they needed maximum points to keep their hopes alive of wrestling the title from Gor Mahia, but they had to go past the unpredictable Brewers who are targeting a top-five finish.
It was the visitors who drew first blood in the 22nd minute. David Naftali's header was saved by Farouk Shikalo, but the defenders were not there to clear the danger, giving Eugene Asike a clear path to score.
However, the lead lasted for only 10 minutes. In the 33rd minute, Abdalla Hassan released a fierce shot, but it was deflected to Ugandan striker William Wadri who did well to cut it back for Shaban Kenga. The latter made no mistake from inside the six-yard area.
The half-time whistle came at a better time for Tusker who looked jaded.
The hosts were not to wait long for circumstances to change, as they went ahead for the first time in the game a few seconds after the restart. Goalkeeper Emery Mvuyekure's miss-kick gave Yemi Mwana possession in the danger zone, and the Congolese danced all the way to the net.
The third goal for the Dockers came late into the game courtesy of substitute Benjamin Mosha. The Brewers conceded a free-kick in a dangerous area, Hassan took it and the goalkeeper parried it as far as Mosha, and the forward banged the ball home.
Bandari are now second on the log with 58 points, eight behind Gor Mahia who have an appointment with bitter rivals AFC Leopards this Sunday.