The 25-year-old dumped Cornish to the canvas twice to earn an emphatic victory and stretch his unbeaten record as a professional to 14 fights.
Cornish, from Inverness, had gone into the bout with a 21-fight unbeaten record and had high hopes of becoming the first man to defeat the Olympic super-heavyweight champion.
But while the 28-year-old showed plenty of intent to attack from the opening bell his admirable ambition simply played into Joshua’s hands.
The home favourite dumped Cornish to the canvas for the first time with a short right hand from which the underdog did well to rise to his feet.
It was all over moments later as Joshua stepped in with a short left to leave Cornish on his knees and earn the first significant title of his career after just over a minute and a half of work.
“It was a perfect connection and he went tumbling down,” said Joshua.
“If I take my time, it could be me on the end of one of those blows in five rounds or so.”
Joshua will next face fellow Londoner Dillian Whyte, who extended his own unbeaten record to 16 fights with a third-round stoppage of Brian Minto on the undercard.
His fight against Whyte, which promoter Eddie Hearn confirmed would take place at the O2 Arena on 12 December, will be for the Commonwealth and vacant British title.
Whyte defeated fellow Londoner Joshua in the amateur ranks and taunted him during the build-up to Saturday night’s show, calling him a “scumbag” and a “fake”.
Consequently, Whyte was booed into the ring before putting on a one-sided, yet ragged, display against his 40-year-old American opponent. Minto, a former cruiserweight world-title challenger, was floored by a straight right hand at the end of the first round and was down again at the start of the third. The initial damage was done by a right hand behind the ear, before a left finished the job.
Minto required attention from paramedics, but walked away from the ring unaided. “It wasn’t the cleanest display, but I did get the job done,” said Whyte, 27, who is now undefeated in 16 pro-contests.
“I was carrying a heavy shoulder injury. But I’ll show up in December, don’t worry about that, even if I am on one arm or one leg. I know the Joshua fight is going to be a good, hard fight but I’m in the game to put on good fights and test myself.”
Joshua was asked whether Whyte’s victory over him in the unpaid ranks had any relevance. “Of course, he’s one-nil up,” Joshua said. “So it’s nice to have the chance to even the score.”