Witnesses told the Harris County Sheriff's Office that the driver drove around the guard rail and attempted to cross the tracks late Wednesday night. The train engineer blared his horn but couldn't stop in time.
The three victims — two males and a female — died at the scene, about 10 miles east of Houston. Authorities said they appeared to be younger than 20.
"The engineer saw the car for a split second before he hit them and he tried to stop by applying the emergency brakes," said Lt. Darryl Coleman, a Sheriff's Office spokesman.
The train continued pushing the car about 2,000 feet before it came to a stop. Coleman said the engineer noticed the car was on fire and backed up trying to detach the car, but it was stuck to the front of the locomotive.
The train's crew used fire extinguishers to put out the car fire.
There were no injuries on board the train, which was carrying 66 passengers on a route from New Orleans to Los Angeles, said Karina Romero, an Amtrak spokeswoman.