Relebohile Mofokeng first struck four minutes into the contest when Lucas Suarez slipped up and failed to stop Evidence Makgopa from crossing for the youngster, who beautifully connected into the net to hand Orlando Pirates the lead.
A minute later, some shambolic defending by Mamelodi Sundowns was witnessed again, with Suarez involved again and Mofokeng took advantage to hit the inside of the post before the ball nestled into the back of the net.
Khuliso Mudau then pulled one goal back for the Brazilians with 21 minutes to go after finishing an Iqraam Rayners long cross.
It was some revenge by the Soweto giants, who were beaten 4-1 by Masandawana in the reverse league fixture in February.
Sunday's 2-1 win saw second-placed Pirates closing in on log leaders Sundowns to 15 points and the Buccaneers have four games in hand.