10:42 AM PT -- TMZ Sports has obtained the arrest video from the prostitution bust ... and it's clear as day Gainey offered $60 for sex acts to an undercover officer posing as a prostitute.
During the exchange, captured by a hidden surveillance camera, Gainey negotiates a price for a "quick visit" and then tells the officer he's in town "the rest of the week" -- clearly implying he could be a repeat customer.
According to the police report, obtained by TMZ Sports, after Gainey handed over the cash, cops busted in and arrested the golfer ... and it sounds like something you'd see on Dateline.
The video is obviously embarrassing and serves as a reminder as to why Robert Kraft is fighting like hell to keep video from his prostitution case under wraps forever.
Pro golfer Tommy Gainey -- famously known as Tommy "Two Gloves" -- was arrested in a major prostitution sting in Florida ... TMZ Sports has learned.
The 44-year-old was 1 of 124 people busted in an undercover investigation in Polk County, Florida dubbed, "Operation Santa's Naughty List."