Randall told NBC10 Boston: "'I kind of looked over and saw what I thought was somebody asleep at the wheel and I was like that can't be right, so I did a double take, looked over and sure enough this guy was just, head between his legs completely asleep."
Randall says the car was traveling 88km/h to 96km/h, and he drove alongside the vehicle for up to a minute.
He says he even honked a couple of times to try to wake the driver before overtaking the car.
Some Twitter users called the video out as "staged", noting that Randall works as a content producer for a regional sports cable television network.
Others claimed that the video showing the autopilot saving lives, with one Tesla fan writing: "People fall asleep behind the wheel, it's a thing that happens. When it's not a Tesla, you have no opportunity to record and post it, because the vehicle immediately crashes into other vehicles, structures, or pedestrians. Thank you again Autopilot for saving even more lives."
Though Randall didn't call police, Massachusetts State Police said they were aware of the video.
A police spokesperson said: "Numerous outlets have contacted us about a video a private citizen posted yesterday showing the driver of a vehicle on the Massachusetts Turnpike apparently asleep or unconscious at the wheel.
"Neither the man who shot and posted the video, nor anyone else, reported this observation to the State Police. Likewise, we received no reports of any crashes in the relevant time frame involving a vehicle matching the description of that in the video.
"Our review of the video available on open source media does not reveal a licence plate on the vehicle. We have reached out to the man who [according to media reports] shot the video to see if he has any further information, including but not limited to a licence plate.
"We have not had a response yet. We will update you if more information becomes available."
A Tesla spokeswoman declined to comment on the video.
- Additional reporting, AP