They were so close that a thrust of a tusk and it could all have been over very quickly. But the couple appeared oblivious to the danger they faced.
Even when the elephant mock-charged them, stopping just a metre from their car, they laughed.
The couple, believed to be from South America, were not the only fans who have been disobeying national park rules and approaching dangerous animals.
"It is terrible; they just get out and start clicking," said a park official, who did not want to be named.
The incident with the mock-charging elephant happened on Tuesday in the Pilanesberg nature reserve and was witnessed by tour operator Bruce Munro.
"They were just ahead of me. They saw the elephant and climbed out of their vehicles. The couple sitting on the roof of a black car drove right up to the elephant," said Munro.
The woman, said Munro, then turned her back on the elephant, which was just 10m away, so her partner could take a photo of her. The elephant, clearly annoyed, pretended to charge the car, he said.
"They did not know how close death was and, sadly, everyone thought it was so funny," Munro said.
In another incident this week, a ranger had to push a fan back into a minibus after he refused to get back into the vehicle.
When the park official challenged the South African tour operator who was driving the bus, the man simply shrugged.
"Over the past two weeks it has been mad - just kombis. And they are treating this like a zoo," the park official said.
It appears other game reserves have experienced similar problems.
In the Kruger National Park last week, tour operator Craig Milner watched a group of tourists standing out of their vehicles for a close look at a pride of lions.
