The Broncos running back was pulled over in Denver late at night on Oct. 13 after cops say they clocked him doing 71 MPH in a 35 MPH zone.

In police footage of the ensuing stop ... you can see Gordon told a cop he had been driving fast because he was just miles from running out of gas.

Just seconds later, Gordon then admitted to an officer he had been drinking before driving.

The 27-year-old told the cop he had "a little bit" of alcohol ... but said he was not drunk.

When pressed by the officer about how much and what he drank, Gordon said he had "just one" drink of Pinot Grigio.

The officer then conducted field sobriety tests -- and you can see in the clip, it appeared Gordon could not walk in a straight line very well.

Cops then put the NFL player in cuffs and asked if he'd take a blood test to see if his blood alcohol content level was below the legal limit.

That's when Gordon admitted again that he had been drinking before getting behind the wheel.

"I've been drinking," Gordon said ... with one officer responding, "I know, I can tell."

Gordon continued, "I got some people that can drive me. I'm not going to lie to you. I play for the Broncos. Obviously, you probably know. And, I cannot risk getting in trouble. I live three minutes from here, probably four."

Gordon and the cop went back and forth over the tailback taking a blood test, with Melvin asking the cop repeatedly if the stop would hit the news.

"I'm scared to get in trouble, bruh," Gordon said. "I ain't going to lie to you, I'm in a f***ing position battle, bruh. I'm lowkey scared, bruh. Please, bruh."

According to police docs, Gordon ultimately did take the blood test ... and prosecutors later hit him with 2 charges of DUI and one count of speeding 25-39 MPH over the limit.

Gordon, though, pled guilty to reckless driving Wednesday, and prosecutors dismissed his two DUI charges.

Gordon was ordered to complete 12 hours of community service as well as pay $478.50 in fines.