The referee brought a halt after four minutes of the first round with Craig unable to defend himself from a series of elbows from the Australian.
Pedro dominated from the first bell, trapping Craig against the cage and connecting several times with his knee.
Craig had some success with a few uppercuts but was hurt by a right hand before Pedro finished it on the floor.
Light-heavyweight Craig had defeated Henrique da Silva in his Ultimate Fighting Championship debut in December.
Scotland's Paul Craig fell to his first defeat in the UFC after he was stopped by Tyson Pedro in Las Vegas.