The contest was stopped after Dodson was hit by a big right hand, with blood already streaming from his face.
The 32-year-old had no answer to his opponent's superior power, having lost to Smith on an unanimous decision in their first fight in 2010.
After a cagey opening couple of rounds, Smith sent Dodson to the canvas in round three with a short left to the body.
Dodson recovered and landed a couple of shots of his own in the latter stages of the round, but Smith was able to dominate thereafter, targeting an early cut before finishing his opponent off with the big right hand.
It is the second time that Smith has won the British title.