An adventure-loving substitute teacher from New Jersey fell to her death in the World Trade Center’s Oculus transit hub — toppling off a high escalator while reaching for a hat dropped by her twin sister.

Tragic twins Jenny and Jessica Santos, 29, had been heading for a PATH train home to Kearny, NJ at 5:30 a.m. Saturday morning after a night of partying in the city, law enforcement sources told The Post.

The two women — described by friends as inseparable — may have been jokingly playing with Jessica’s hat as they rode the escalator down to the concourse level.

But when Jenny grabbed for her twin’s hat as it began to fall, she lost her balance, sources said.

As Jessica watched in horror, Jenny plummeted 30 feet, her body striking the white marble of the concourse floor.

Jessica ran screaming to her sister, but her twin died instantly, a shaken witness recounted.

“There was nothing you could do. She wasn’t going to make it,” said a construction worker, who had been heading for work at 4 World Trade Center. “There was a lot of blood, and the way she was laying … That was it.”

The surviving twin was taken to a nearby hospital for trauma, sources said.

Jenny worked as a substitute teacher at both grammar and high school levels, and was well-traveled and well-liked, according to friends and her social media.

“She was very caring, very involved, very close to her family. A very happy person,” said one friend outside the family’s Kearny home, where the twins still lived with their mother.

“The sisters were very close,” the friend added.

“One wouldn’t do one thing without the other.

The friend said the surviving twin is “devastated.”

“My daughter spoke to her on the phone this morning — she was hysterical.”

Jenny graduated from William Paterson University of New Jersey with a BS in physical education and health for kindergarten through 12th grade and driver’s education, according to her LinkedIn page.

She’d traveled through Europe and loved the outdoors, according to her Couchsurfing profile, in which she described herself as, “Just trying to live life the best way possible.”

She also wrote of her love of skydiving: “Never felt a feeling of being alive and badass at the same time.”

“Such a tragedy to see a kind, beautiful person gone too soon. One of the best people I’ve had the honor to know,’ friend Brian Reis posted on Facebook. “Some of my most fond memories were spent with you and I’ll never forget it. Rest in Peace Jenny Santos.”

The $4 billion transit hub and shopping mall has been open for just ten months. In October, a woman gave birth to a healthy girl there with help walking from Port Authority cops.

Additional reporting by Kevin Fasick, Melkorka Liceaand Laura Italiano