Johannesburg’s bustling O. R. Tambo International Airport is an easy place to get lost in a crowd, and that’s just what a 29-year-old Vietnamese man named Xuan Hoang was hoping to do one day in March last year—just lie low until he could board his flight home. The police dog sniffing the line of passengers didn’t worry him; he’d checked his baggage through to Ho Chi Minh City. But behind the scenes, police were also using X-ray scanners on luggage checked to Vietnam, believed to be the epicenter of a new war on rhinos. And when Hoang’s bag appeared on the screen, they saw the unmistakable shape of rhinoceros horns—six of them, weighing more than 35 pounds and worth up to $500,000 on the black market.

Investigators suspected the contraband might be linked to a poaching incident a few days earlier on a game farm in Limpopo Province, on South Africa’s northern border. “We have learned over time, as soon as a rhino goes down, in the next two or three days the horns will leave the country,” Col. Johan Jooste of South Africa’s national priority crime unit told me when I interviewed him in Pretoria.

The Limpopo rhinos had been killed in a “chemical poaching,” meaning that hunters, probably in a helicopter, had shot them using darts loaded with an overdose of veterinary tranquilizers.

The involvement of sophisticated criminal syndicates has soared along with the price of rhino horn, said Jooste, a short, thickly built bull of a man. “The couriers are like drug mules, specifically recruited to come into South Africa on holiday. All they know is that they need to pack for one or two days. They come in here with minimal contact details, sometimes with just a mobile phone, and they meet with guys providing the horns. They discard the phone so there’s no way to trace it to any other people.”

South African courts often require police to connect the horns to a specific poaching incident. “In the past,” said Jooste, “we needed to ph...