Justin Bieber -- Gloria Allred Brags About Dave & Buster's 'Evidence'

With Justin Bieber's history of stupid, dangerous, and illegal stunts -- it's pretty amazing he and Gloria Allred's paths are crossing for the first time ... over his alleged Dave & Buster's run-in with a couple.

Allred tells TMZ she's been hired to represent the couple who claim Bieber tried to snatch a cell phone from them last week in the restaurant/arcade.

We broke the story ... police say Bieber lunged at a guy who snapped cell phone pics of Justin and Selena Gomez.

We spoke to Gloria outside LAPD's Hollywood division, and she described her clients' smoking gun -- video of the incident .. which she says they've turned over to cops.

Law enforcement sources tell us, LAPD has reviewed it for evidence of a crime -- and while it does show JB lunging ... he never makes physical contact.