The Buccaneers enjoyed the majority of possession from the start but struggled to find a breakthrough before half-time, with Bafana Bafana international Oswin Appollis forcing Chippa goalkeeper Stanley Nwabali into a number of saves.
Chippa United resorted to long-range speculative attempts in the first half, with efforts from Sirgio Kammies, Abbubaker Mobara and Goodman Mosele missing the target.
AmaBhakaniya started to apply more pressure at the start of the second half and were duly rewarded at the hour mark when Ghampani Lungu latched onto a Patrick Maswanganyi pass to put a solid near post-strike past Nwabali.
The visitors doubled their lead just four minutes later through a header from defender and Man of the Match Lebone Seema to leave United’s hopes for a result in tatters.
A defensive mistake in the 87th minute allowed substitute Daniel Msendami to dispossess the last defender before cooly slotting in for the third goal of the match, sealing the three points for the Soweto giants.
The result sees Pirates leapfrog rivals Kaizer Chiefs to the top of the league table due to superior goal difference after three games played.