A Washington Wizards fan socked a Boston Celtics fan in the face at the TD Garden during Game 7 -- dropping the dude into the seats ... while nearby fans cheered them on. 

Unclear what started the fight, but the man in the John Wall jersey reached back and clocked the dude -- while the victim was still clutching his cell phone.

Another Celtics fan tried to jump in and help out his fallen comrade ... but the damage was already done.

We spoke with cops who say no one was arrested at TD Garden on Monday. 

Meantime, we got a photo of the aftermath ... it was bloody.