Goals from Gilbert Mushangazhike and Lucas Thwala in the first half secured Pirates their first victory over Chiefs in official competition since October 2004, and gave Dutch coach Ruud Krol all three points in his Derby debut.
For Chiefs' Mushin Ertugral, it is a bitter blow. His side had come into the game on the back of three straight wins in the league, but this result will throw further doubt over their ability to mount a creditable challenge for the title.
Pirates signaled their intention from within the first minute, as a swerving long-range effort from Teko Modise almost wrong-footed Chiefs' Itumeleng Khune.
A minute later the goalkeeper made a fantastic acrobatic save to grasp Mushangazhike’s goal-bound header from a cross by Dikgang Mabalane.
The Amakhosi should have opened the scoring in the fifth minute, but David Mathebula couldn't decide on whether to shoot or cross from a tight angle and in the end did neither, blowing a fine opportunity.
Gert Schalkwyk was also guilty of dithering in possession when he found himself through on goal in the 12th minute, but the Pirates defence got back to rob the midfielder of the ball.
Schalkwyk appealed for a penalty, but he only had himself to blame for not pulling the trigger earlier.
Just after the 20 minute mark the game had a short break while one of the assistant referees received treatment for what looked like a calf strain. Upon restarting it was clear that Chiefs' concentration had been disrupted, as they immediately conceded the opening goal.
Mabalane found some space down the right flank and whipped in a fine cross, matched by Mushangazhike’s intelligently steered header back across the face of goal that found the bottom corner.
Just over ten minutes later Pirates doubled their lead, Thwala scoring from close range with a towering header after another pinpoint cross from Mabalane.
The Amakhosi were still dangerous on the break, however, and it took a desperate block from the back-tracking Mabalane to deny Reneilwe Letsholonyane after the midfielder had found himself through on goal and faced only with Senzo Meyiwa to beat.
Ertugral knew that his team needed a reshuffle to try and spark a comeback, and he duly introduced both Jimmy Tau and Thuso Phala at the start of the second half. However, the substitutes were unable to save their team from defeat.
Just past the hour mark Meyiwa was called upon to make his first genuine save, stooping low to grasp Schalkwyk's header after a good ball into the penalty area from Mathebula.
Modise, who had dictated the game all afternoon, twice came close to making it 3-0. First, in the 72nd minute, he beat Khune with a low drive but not the upright, and he was unable to steer the ball on target from the rebound.
Then just three minutes later his free-kick from the right flank flashed across the face of goal, needing just a touch to divert it into the back of the net.