Law enforcement sources tell us ... cops responded to the church around 1 AM after receiving a tip about two men fighting in the parking lot.

Once officers arrived to the scene ... both men were taken to the hospital. One source tells us Randy appeared to be "extremely intoxicated." We're told the fight was over a girl.

Travis has had serious problems with alcohol -- he was arrested for DUI earlier this month after cops say they found the singer naked at the scene of a car crash.