South Africa Rugby Union has apologised to New Zealand over "highly regrettable" disruption to the closing stages of their haka before the hosts' Rugby Championship victory on Saturday in Johannesburg.

As a mark of respect, traditionally the opposition would remain silent and allow New Zealand to perform the haka.

However, at Emirates Airline Park, the final moments were overlaid by music and fireworks, as well as a flyover by an A380 airline caused by "timekeeping challenges" and "simple human error", according to SA Rugby chief executive Rian Oberholzer.

"I apologised in person and have written to the NZRFU to formally express our regret and apologies for what occurred," added Oberholzer.

"It was never the intention to schedule any activities that would coincide with such an iconic moment of any Test match against the All Blacks.

"In the confusion, the crowd's excited cheering was mistaken to have marked the conclusion of the Haka by an unsighted sound engineer who restarted the music programme.

"It was highly regrettable but in no way deliberate."

Grant Williams' late try rounded off a stunning 31-27 comeback victory in Johannesburg to make it three wins from three for the Springboks in the Rugby Championship.

The two sides play again on Saturday at DHL Stadium in Cape Town.