The WBA inter-continental clash went the Russian's way as he finished it with a devastating right and left hand combination, sending Price crashing to the floor.
It was Povetkin's 34th victory in 35 fights, and as the WBA mandatory challenger, he now looks set to fight Anthony Joshua or Joseph Parker.
Price, 34, had targeted what he termed a life-changing victory by toppling Povetkin.
Povetkin, though, was the clear favourite to win, and he ultimately delivered, even if Price gave it everything.
Price made a confident start, absorbing a couple of shots from Povetkin before landing two of his own, with the second one clearly ruffling the Russian.
And he continued confidently in round two, bossing the centre of the ring and giving Povetkin plenty of food for thought.
But things began to unravel in round three when Povetkin landed a blistering left hook that floored Price and left him nursing a cut above his left eye.
Price, though, responded superbly as he sent Povetkin stumbling backwards just as the bell sounded to end a thrilling three minutes, and both fighters knew the contest was hurtling towards an early conclusion.
Povetkin seemed unsteady on his feet at the start of round four, and Price continued to give as good as he got, but the Russian had a mighty finish in his locker.
He rocked Price with a right hand, and then with his opponent's defence wide open, he landed the punch that ended Price's hopes - and possibly his boxing career.
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