His wife, Arlene, told The New York Times he had been treated for mesothelioma for two years. She said the immediate cause of death was heart failure.
Durk died at his home in Putnam County, north of the city.
With Frank Serpico, a fellow officer who became better known, Durk worked to expose the endemic corruption in New York.
The son of a doctor, Durk joined the police department after graduating from Amherst College and attending Columbia Law School. He said later he hoped to be able to keep the streets safe for ordinary New Yorkers.
Instead, he found that police officers were taking payoffs to overlook illegal gambling and other crimes with higher-ranking officers getting their share of the take.
Serpico and Durk, who met in a police academy course, both refused to participate in graft and were shunned by many of their fellow officers as a result. The colorful Serpico lived in Greenwich Village, where he was known to his friends as Paco, wore a serape and was married four times and divorced three, otherwise had little in common with Durk, a family man who lived on the Upper West Side.
The two officers tried to go through channels, complaining to high-ranking city officials. Eventually, they met with a Times reporter, who wrote a series on police corruption.
An investigation was followed by the conviction of dozens of low-ranking police officers. But the top brass and city officials were left largely unscathed.
Serpico became the subject of a best-selling book and a movie, "Serpico," starring Al Pacino. But many observers said Durk's role in their quest was at least as big.
Mary Perot Nichols, who headed the New York City government radio and TV stations, said Durk, who knew people in the news business and kept up the pressure, was more responsible for opening up the scandal.
"It would be fair to say that without Durk, there would have been no police corruption expose in The New York Times, no Knapp Commission investigations into the matter,"Nichols wrote in the Times.
Serpico, who was shot in the face in a drug raid in 1971, left the department in 1972 and lived in Europe for eight years. He now lives in upstate New York.
Durk remained a police officer until 1985, when he retired. His later career was a mix of investigations that were often stymied and of being shunted aside.
"Corruption is not about money at all, because there is no amount of money that you can pay a cop to risk his life 365 days a year," he said in testimony before the Knapp Commission. "Being a cop is a vocation or it is nothing at all, and that's what I saw destroyed by the corruption of the New York City Police Department, destroyed for me and for thousands of others like me."