BYU Running Back Jamaal Williams -- ARRESTED FOR BOOZING ... Was In Car with Sober Designated Driver

BYU running back Jamaal Williams was arrested for underage drinking in Utah recently ... despite the fact he was in a car, on his way home, with a sober designated driver behind the wheel.

TMZ Sports has learned ... the 18-year-old sophomore (a rising star who's expected to start next year) was a passenger in a car that was pulled over for speeding around 2am on February 16.

Law enforcement tells us ... the officer approached the car and smelled booze and decided to test the driver and the two passengers, because all of them appeared under the age of 21.

Cops determined the driver was 100% sober -- but Williams blew "about a .12" on the breathalyzer ... and was immediately cited for misdemeanor underage drinking.

Williams appeared in court in Utah this week and plead not guilty to the charge, He's schedule to appear in court in May.

Jamaal's football career at BYU could be in jeopardy -- since a conviction would be a violation of the school's honor code ... which the university has been known to enforce.