Unbeaten Joshua dominated from the start but the 30-year-old Breazeale proved a courageous opponent, absorbing some thunderous blows throughout from the 2012 Olympic super-heavyweight champion before succumbing to Joshua's power.
There were signs that Joshua was beginning to get frustrated in the sixth round of his first title defence but he began the seventh with a tremendous barrage of blows that sent his opponent to the canvas.
Breazeale, also unbeaten prior to the bout, managed to continue but was floored again by a left and the referee waved an end to the contest without counting.
Joshua took his record to 17-0, all by knockout or stoppage, and his classy display offered more evidence to support the belief that the muscular 26-year-old could eventually unify the division.
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"When you start catching them flush, you know they can feel the shots, and so he was tough," Joshua, who won the title by beating Charles Martin in his previous fight, told reporters.
"But this has been tough for me, as two weeks after my last fight I was straight back into the ring. So now I look forward to getting my break. I need some time off."
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Joshua wobbled Breazeale in the second round with a right hook and again with a stinging shot to the body.
A cut and opened up above Breazeale's swollen eye in the third but the American was still throwing punches, even if few of them found their target.
Joshua dominated the fourth round, although Breazeale did connect with a straight right to the top of the champion's head in the fifth, exchanging words with the Briton at the bell.
Breazeale drew blood from Joshua's nose in the sixth and ended the round on the front foot but the Briton nailed him in the seventh.
"I'm making waves in the U.S. now and one day I'm sure (WBC holder) Deontay Wilder and I will get to experience what each other are all about," Joshua, who wore white in memory of heavyweight great Muhammad Ali, said.
"Ali is an inspirational person, inside and outside of the ring. It will take time to get anywhere close to that, but all I can do is try. This is my moment and all I can do it take advantage of it."
Joshua's fellow Britain Tyson Fury holds the WBA ands WBO belts and was scheduled to fight former champion Wladimir Klitschko in a rematch on July 9 but pulled out because of an ankle injury suffered in training.
(Reporting by Martyn Herman; Editing by John O'Brien)
