Terrified Rutgers students called cops when a man broke into their dorm in the middle of the night — just days before a similar-looking creep sexually assaulted a sleeping student in her room on Sunday, The Post has learned.

Police said they were stepping up patrols at the Piscataway, NJ, university in the wake of the early-morning assault, but female students say they fear for their safety on campus, carry pepper spray and constantly lock their doors.

One student who didn’t want to be named said he woke up last week to find a similar-looking man in his room in the dead of the night.

“This isn’t the first time this guy has been here,” he said Monday.

“Just the other day I woke up at like 3 in the morning to my roommate screaming at the exact same guy to get out of our room. We called the police too.”

Cops say the attacker went into an unlocked dorm room on the Livingston campus around 7:40 a.m. Sunday and sexually assaulted the female student who was asleep.

When she woke up, the man ran out of the room and fled, according to an alert sent to Rutgers students. She was physically unharmed.

The suspect is described as a 20-year-old Hispanic or Indian male, approximately 5 feet 7 with a thin build and black hair, and was wearing glasses with a pink shirt and blue jeans.

Freshman Suchi Trivedi said people frequently tailgated students into the buildings — with one man sneaking in after her last week when she swiped into her dorm building, telling her, “Oh, I’m just visiting a friend.”

“I always lock my doors and I hope everyone knows to lock their doors,” she said. “My roommate has pepper spray so I always try to just stick with her whenever I go out.”

“It’s easy to get into the buildings. You can just swipe into the dorm and people will walk in behind you.”

A Rutgers University spokesperson would not answer questions about the incident, citing an ongoing investigation.

Freshman LeeAnn Rego echoed Trivedi’s concerns and said students were awakened Sunday by police at their door asking questions after the sexual assault.

“It is scary to think about,” she said. “This campus needs more security, especially here.”

In Quad 2 where the dorm is located, security cameras can be seen fixed to doors and the sides of each building.

The Rutgers University Police Department said it was stepping up patrols in the wake of the assault, but on Monday, a Post reporter observed just one police car stationed next to a pack of media.

“It’s scary to think my dorm is here and it could have been me,” freshman Christina Li told The Post.

The investigation is ongoing.