In a League tie where Stars were unluckily denied a penalty late on, Pirates threatened first as Oupa Manyisa flashed a long-range effort wide in the opening exchanges.
Allan Freese's men, though, stole ahead in the 32nd minute when ex-Buccaneer Mthembu powerfully headed home a left-wing cross by Mduduzi Nyanda to give his side a 1-0 lead at the break.
Bucs had a great chance to equalise 10 minutes after the interval, but Daine Klate placed a rather tame shot in the area straight at Siyabonga Mpontshane, who saved in unorthodox fashion by sitting on the ball.
The Sea Robbers, however, drew level on the hour-mark as Bacela rose above Vuyo Mere to shoulder the ball in with his first touch after replacing Tlou Segolela three minutes earlier.
Bacela pounced from a yard out after Mpontshane failed to get on the end of a Klate corner. The delivery was flicked on by Issa Sarr to Stars teammate Tintswalo Tshabalala, whose miscued clearance found Bacela at the back post.
The visitors should have been awarded a spot-kick in the 82nd minute, but referee Kulasande Qongqo, who was perfectly positioned, waved play on after Nyanda was tripped by Happy Jele in the box.
Pirates then nearly snatched a stoppage-time winner but Mpontshane pulled off a superb acrobatic stop to foil Thabo Matlaba's powerful strike from distance.