Great day for Buffalo Bills running back Jonathan Williams -- who fought his 2016 drunk driving arrest ... AND WON.

TMZ Sports broke the story ... Williams -- a 5th round pick out of Arkansas in 2016 -- was pulled over in Fayatteville, AR on July 14 when cops suspected he had been drinking.

Williams had admitted to drinking a 40 oz. before getting behind the wheel, but refused to take a breathalyzer ... leading to his arrest. He begged cops to give him a pass because he was just drafted into the NFL.

Williams pled not guilty and took the case to trial -- where prosecutors failed to prove JW was driving drunk that night. Why? We're told the lack of a positive blood alcohol test was a factor.