The 36-year-old champion was a cut above the Liverpool fighter, recording his 20th victory by knockout and improving his professional record to 23-1 in the process.
It was a game effort from the challenger, who was watchful in the opening round, content to settle into the contest and avoid any early mistakes.
Meanwhile, Stevenson, as expected, took the front foot and pressed his opponent around the ring.
Both men found the mark with decent shots, and although Bellew perhaps landed the best, it was the Canadian who did enough to take an early lead on the scorecards.
Stevenson continued to pressure early in the second, but walked onto a good combination. It did not faze him, as he continued to dictate the pace, catching with a left that landed bang on the button.
'Superman' was outworking Bellew, and anything that Bellew did manage to land was being beaten.
The action stepped up a gear in the third, with Stevenson backing Bellew up with a string of hard lefts that brought the crowd to their feet; still the challenger moved, looking for an opportunity to strike.
Heightened aggression in the fourth round brought some success for Bellew, and the crowd were aghast when he had Stevenson on the deck.
However, the referee correctly ruled it a slip, although the 31-year-old challenger seemed reinvigorated.
It was not to be, though, as the beginning of the end came early in the sixth, with a big left from Stevenson sending Bellew on his backside.
'The Bomber' shook his head, seemingly angry with himself, after getting to his feet, but the referee had to step in to save him when Stevenson rained in another stiff left that dazed him in the corner.
It is only the second defeat - and first stoppage - of Bellew's 23-fight career, with his previous loss also being in a world title fight against Nathan Cleverly in 2011.