An own goal by Ntsikelelo Nyauza, Leonard Castro and a Daniel Cardoso penalty gave Amakhosi the win while Vincent Pule and Gabadinho Mhango replied for Pirates, who lost for the first time to their fierce rivals in the PSL since December 2014.
Chiefs took a sensational lead just 45 seconds into the contest as Pirates captain Nyauza put the ball into his own net after a calamitous mix-up with his goalkeeper Wayne Sandilands.
The Buccaneers almost hit back immediately as Fortune Makaringe struck a rasping long-range shot against the post that had Chiefs keeper Daniel Akpeyi well beaten.
Chiefs midfielder Willard Katsande was lucky to stay on the pitch as he delivered a shocking knee-high challenge on Makaringe after 10 minutes that the referee only deemed worthy of a yellow card.
The Glamour Boys were the better side though and it came as no surprise when they doubled their lead as Castro sent a powerful header past Sandilands in the 28th minute from a George Maluleka corner.
Pirates were now forced to raise their game as they searched for some answers and Pule gave them a lifeline six minutes before the half-time break as the winger rifled in a free-kick from a tight angle.
The Buccaneers were the better side at the start of the second half and started to dominate proceedings with Thembinkosi Lorch hitting the woodwork from point-blank range in the 52nd minute.
The men in white and black must have thought that it wasn't going to be their day as Pule then struck the cross-bar when he came one-one with the Chiefs keeper.
Pirates deserved to be level at that stage and the equaliser duly came just before the hour mark as Mhango sent a beautiful curling effort into the top corner that Akepyi had no chance of saving.
It seemed the momentum was the Buccaneers with Chiefs failing to get the control they had in the first half.
Pirates failed to carve out any clear-cut chances for the third goal though, and Chiefs, on of their few attacks, were awarded a penalty eight minites form the end of the normal time when Parker was clumsily fouled by Paseka Mako.
Cardoso converted the spot-kick to give Chiefs the lead but the drama was far from over as Chiefs were reduced to 10 men close to the end after Eric Mathoho was sent off after he was adjudged to have shoved Abel Mabaso.
Amakhosi hung on for the three points though in one of the better Soweto derby's in recent memory.