Two drug-addled thieves in wigs and women’s clothing stole an SUV and then made a wrong turn into the entrance of the National Security Agency headquarters near Washington, DC, Monday — a decision that turned fatal when the driver plowed into the security gates, forcing guards to open fire, sources said.

The NSA officers guarding the Fort Meade, Md., base killed one of the men and severely wounded the other as they attempted to storm the gate with ​a Ford Escape just before ​9 a.m., the agency said in a statement.

Law enforcement sources described the gate-crashers as transvestites who had a gun and cocaine in the vehicle, which they had robbed from a hotel in the nearby town of Jessup, Md., after a night partying there with a male friend.

The men took a wrong exit while making their escape along the Baltimore-Washington Parkway and drove up on the police officers and heavily guarded barricade. The driver in drag panicked and floored the accelerator in an effort to get away, the source told The Post.

As the SUV came speeding toward them, officers opened fire on the cross-dressers, causing them to crash into an NSA police vehicle that was blocking the road.

One died at the scene and the other — identified as Kevin Fleming of Baltimore — was rushed to a hospital ​with ​potentially fatal injuries, sources ​said.

Fleming reportedly has a lengthy criminal record, including for assault, theft and eluding police.

The NSA officers only used deadly force against the two men after they refused to obey “routine instructions for safely exiting the secure campus,” the agency said in its statement.

The cause of death has not yet been determined for the suspect who died. A 44-year-old male NSA police officer was taken to the hospital with non-life-threatening injuries, authorities said.

Photos taken from chopper video at the scene show a white sheet covering what appears to be a body lying in the middle of the road next to the heavily damaged SUV. A banged-up white police SUV can be seen alongside an ambulance.

In one image, a brown wig presumably worn by one of the shooting suspects lies in the roadway amid scattered debris.

Fort Meade is a US Army base in Anne Arundel County, Maryland, and lies northeast of the nation’s capital. Around 11,000 military employees and 29,000 civilians are employed there and about 6,000 people actually live on the base, according to the Army.

A 35-year-old former correctional officer was arrested earlier this month and accused of firing a gun toward five public places in Maryland after the NSA reported damage to one of its buildings from gunshots.

With Post Wire services