Justin Timberlake's BMW on Video Driving Down Sag Harbor Street Before DWI Arrest

TMZ has found video that shows Justin Timberlake cruising down the street in Sag Harbor early Tuesday before he was pulled over by cops and arrested for DWI ... and based on what he told police, it appears he was following some friends who were leading the way.

Check out this footage we tracked down from surveillance cameras in the area ... it captures a black sedan heading south on Main Street -- a block away from the American Hotel, where Justin left moments earlier -- and a second or two later, you see JT's vehicle pop into frame.

The vehicle matches the description cops gave in their police report to a T -- a gray BMW UT -- and you can see Justin was following closely behind on the road ... not necessarily swerving or driving erratically, at least not in this clip anyway.

About half a mile from where this video was shot ... cops say they saw Justin blow past a stop sign -- at which point they started to follow him for about another half mile or so.

Per the report ... cops say they observed Justin failing to stay in a straight line while driving, and eventually, they pulled him over ... when they claim they suspected he was driving under the influence based on a number of signs they say they witnessed while talking to him.

All in all ... Justin drove a little over a mile from the hotel before he got stopped, and ultimately -- he was arrested and booked for driving while intoxicated. The police claim Justin told them that he just had one martini, and that he was following friends home.

That jibes with what sources told us about this whole thing -- namely, that JT's friends attempted to intervene in the arrest ... asking cops to cut him a break.

Justin has since been arraigned and released on his recognizance ... and photos of him leaving the courthouse there in town have surfaced.