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The 31-year-old Briton was close to winning when he floored Pulev in the third round after a sweet right hand, but the challenger recovered to test the home favourite in front of a limited crowd of 1000 in London on Saturday.
Pulev (39) remained dangerous, without causing Joshua many anxious moments, but there was no escape in the ninth.
Joshua landed a clubbing right upper-cut which sent Pulev to the canvas.
The Bulgarian got back to his feet but Joshua connected with another huge right hand to end the contest.