The overnight assistant manager told Fox News she recently had some downtime, so she reviewed the gas station's surveillance video from around the time of the November 13 early morning attacks. Despite not working that day, she said she had a "weird feeling" to go look at the footage.

It paid off ... she found a snippet that showed a white sedan barreling down the highway and turning onto a side street. The vehicle matches the description of a 2011-2013 white Hyundai Elantra police have been searching for since last week. Cops say they want to speak with the occupant(s) of the car, which was spotted near the crime scene the night of the slayings.

The gas station manager snapped a screenshot and emailed it to investigators through a tipline. Detectives went to retrieve the new evidence and are now pouring over hours of footage, trying to find more clues. They don't know yet if the video shows the actual car they're seeking, as they haven't been able to match license plates.

Moscow PD spokesperson Robbie Johnson tells TMZ ... they are having difficulties locating the Hyundai because the car is so common, but they have received "good tips." Neighboring police departments are also keeping an eye out for the car. Pullman PD, which is about 7 miles from Moscow, tells us they are "closely scrutinizing" all vehicles that look like the Hyundai.

As we reported, 4 University of Idaho students -- Kaylee Goncalves, Madison Mogen, Xana Kernodle and Kernodle's boyfriend, Ethan Chapin -- were discovered fatally stabbed inside an off-campus house last month.