Tommy "Two Gloves" Gainey is a real crappy criminal ... but the dude sure can golf -- 'cause just 4 days after he was arrested for soliciting a prostitute -- he CRUSHED it on the course!
Despite being busted on Dec. 8 for trying to pay an undercover officer for sex acts ... Gainey still dominated the first day of the final stage of Korn Ferry Tour Q-School in Florida on Thursday.
Taking on the Orange County National course in Winter Gardens, Florida ... Gainey went SUPER low, shooting a 6-under 66 -- and finishing his round in a tie for 6th place.