In the first half, the inspired Elvis Chipezeze pulled some great saves to deny the Soweto giants, who were determined to avenge the 3-2 loss last season that saw them crash out in the initial hurdle.
Yanela Mbuthuma had three excellent attempts that the Zimbabwe international dealt with effectively. The custodian was finally beaten in the 28th minute, but the former Richards Bay man was denied by the crossbar.
Dikwena Tsa Meetse were lucky to end the first half without conceding, while Bucs felt unlucky not to have found the back of the net.
After the break, Chipezeze, once again, forced Oswin Appollis' effort against the crossbar in the 50th minute, but the custodian had no response a minute later as Tshepang Moremi's rocket flew past him to give Bucs a deserved lead.
The visitors thought they had leveled through Abbey Seseane, but despite doing everything right, the woodwork denied him.
Evidence Makgopa then doubled the advantage with a minute to go with a well-taken goal.
Lehlogonolo Mokone scored late in the game to give Magesi hope but the damage had already been done.
Abdeslam Ouaddou's men are now into the last four of the Carling Knockout.