The incident happened near Nashville back on Nov. 18, 2022 at around 2:30 AM ... just hours after Downing had helped lead Tennessee to a big "Thursday Night Football" win over the Green Bay Packers at Lambeau Field.

In dash cam footage, you can see a Tennessee Highway Patrol trooper pulled behind Downing's Mercedes on a freeway ... and said the 42-year-old was "hauling ass" -- going over 100 MPH "easily."

Body cam video shows when the officer eventually stopped Downing and began questioning him ... the coach apologized for being in a hurry -- explaining that he was trying to get home to his family because "I got a death threat tonight."

The officer, though, said he smelled an odor of booze coming from Downing's car. Todd responded that he hadn't been drinking, but when he got out of the ride for sobriety testing, he changed his story, saying, "I had a victory beer in Green Bay."

Downing then underwent several field sobriety tests, and according to the trooper, he failed them. He was placed under arrest for DUI.

When he was put in the back of a squad car, he made a call to a member of the Titans' organization, telling him what had just happened.

"Hey, man, I was rushing home and I got arrested for DUI," Downing said. "I was panicking because I was scared about my family -- and I had a victory beer."

Downing then told the man he'd prefer to tell head coach Mike Vrabel about the arrest himself.

Downing -- after pleading with the officer for "grace" -- was transported to a medical facility to get his blood drawn, before he was booked at a local jail.

He went on to serve a 48-hour sentence behind bars in January to close out the case.