Van der Burgh charged through the first lap at breakneck speed then held off his challengers in the last length to reach the wall in 58.46 seconds.
His time trimmed 0.12 seconds off the previous world record of 58.58 set by Australia's Brenton Rickard at the 2009 world championships in Rome before polyurethane bodysuits were banned.
Australia's Christian Sprenger took the silver medal in 58.93 while American Brendan Hansen was third as an exhausted van der Burgh lay down on the lane ropes to celebrate his win.
He became the first South African man to win Olympic gold in an individual swimming event.
Japan's Kosuke Kitajima, who won the breaststroke double at Athens in 2004 and Beijing four years later, was fifth, missing his chance to become the first man to win the same individual swimming title at three successive Olympics.
He still has the 200 breaststroke later in the programme.
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