The Buccaneers came into the contest following a heartbreaking penalty shoot-out defeat against Saint-Eloi Lupopo in the CAF Champions League on Saturday.
The Soweto giants wanted to assert their dominance against the defending champions and took the game to visitors in the first half.
Pirates had numerous opportunities to take the lead but visiting goalkeeper Elvis Chipezeze seemed to be having an unforgettable game to date as denied Yanela Mbuthuma point-blank range.
Mbuthuma was causing havoc upfront but lacked the finishing touch as the forward also hit the cross-bar while Chipezeze remained an immovable force.
Magesi were content to play on the counter-attack and had a few chances of their own as they found the home team's defence lacking in certain stages as the teams went to halftime with the score goalless.
The deadlock was broken six minutes after the interval though as Moremi produced something special that finally beat Chipezeze and found the top corner.
The visitors did not go down without a fight though and came inches from an equalier when Abbey Seseane struck the woodwork.
Pirates continued to push forward and the hosts got a second with three minutes remaining when Evidence Makgopa showed his finishing prowess.
Magesi did get on the scoreboard in stoppage-time with a late header but it mattered little as Orlando Pirates went into the last four of the Carling Knockout Cup.
