Surveillance footage obtained by The Post shows the moment an off-duty NYPD sergeant shoots a Brooklyn man with whom he’d been feuding over a woman.

The nearly minute-long clip begins with the cop, Sgt. Ritchard Blake, appearing to argue with Thavone Santana under the elevated Livonia Avenue train tracks in East New York around 5 a.m. Thursday.

As the spat escalates, Blake pulls out a gun, Santana recoils and starts to turn away, then falls to the ground on his right side, the video shows.

The clip then shows the 40-year-old cop pacing around Santana for a few seconds before bending down to place an object — which law enforcement sources said is a knife — next to his torso.

Blake turns his back on the 21-year-old victim, appearing to hold his cellphone to his ear, before turning back to Santana and picking up the apparent knife before the video cuts out.

When his fellow cops showed up, Blake told them that Santana had tried to rob him, sources said.

But the two men already knew each other, and had an ongoing dispute over a woman — who shares a 10-year-old son with Blake, according to sources.

Santana, shot once in the jaw, underwent multiple surgeries and is expected to survive.

Blake, assigned to the 109th precinct in Queens, has been stripped of his gun and badge pending an investigation.