It was a bizarre love story that gave birth to the NYPD’s hostage negotiation team.

Thanks to Hollywood, it’s also a familiar one: “Dog Day Afternoon” robber John Wojtowicz wanted cash to cover his boyfriend’s sex-change surgery when he burst into a Brooklyn bank Aug. 22, 1972 — 40 years ago today.

The rifle-toting robber was played by Al Pacino in the Oscar-winning movie — but to Officer Harvey Schlossberg, the real stars were the cops who helped Wojtowicz’s hostages escape unharmed.

“They were able to talk him into the idea that they could get him an airplane,” Schlossberg, now a professor at St. John’s University, told the Daily News.

“It was clear he was not ready to die . . . he was looking for a way out.”

Schlossberg — at the time a recent Yeshiva University graduate with a Ph.D. in psychology — noted the officers’ techniques in brokering a deal to protect the bank workers.

He became convinced there was a way to talk a person out of a hostage situation, eliminating the need for tactical force and saving lives.

NYPD brass, already spooked by the Attica prison riots that left 34 dead a year earlier, began serious talks with Schlossberg

Two weeks later, the world stopped to watch the horrifying events unfold in Munich, West Germany. Members of the Israeli Olympic team were taken hostage and later killed .

Schlossberg began working with Lt. Frank Bolz to draw a set of guidelines dealing with hostage negotiations. The pair became the first in law enforcement history tailored to converse with people threatening to harm themselves or others.

In January 1973, they were called to a Williamsburg, Brooklyn, business where four men were holding a dozen people hostage after a botched robbery.

Police arrived at John and Al’s Sporting Goods Store, where one bandit had already shot and killed Officer Stephen Gilroy. “I had to calm them,” Schlossberg recalled.

The standoff ended 47 hours later with all four suspects in cuffs. The ordeal left Gilroy dead and two other cops wounded. But none of the hostages were hurt.

The following March, 28 cops from the detectives bureau graduated as the first hostage negotiations team.

Nearly 40 years later, Lt. Jack Cambria, a 30-year vet and the unit’s commanding officer, said they respond to about 35 jobs every month.

The team — which consists of about 100 seasoned detectives from various commands — are called to several types of jobs that include domestic incidents and people threatening suicide.

“The best negotiators are people with life stories, because they can relate,” Cambria said.

In the original case, the cops ended a 13-hour standoff as a rowdy crowd of spectators gathered outside the Chase Manhattan branch on Avenue P and E. Third St. on a summer afternoon.

Wojtowicz and his armed sidekick, Sal Naturale, held several employees hostage as Wojtowicz demanded loot so he could pay for his male lover’s sex-change operation.

Authorities coaxed the would-be robbers to a plane at Kennedy Airport, where Wojtowicz was apprehended and Naturale was shot and killed by an FBI agent as hostages walked free.

Wojtowicz was sentenced to up to 20 years in prison. He was released after six years, but later rearrested for violating his parole.

Salvatore Antonio Naturale