Klitschko was the only man to have previously inflicted a blemish on Povetkin's now 36-fight record, with a points win back in 2013.
Joshua appeared to be in control in the opener, but Povetkin caught Joshua with a sweet three punch combo at the end of the round.
And he'll likely be taking home even more money in his next fight, with American Deontay Wilder on his radar.
Who do you think Joshua will fight next?
Fury, 30, is the former IBF, WBA, IBO and WBO heavyweight world champion.
"Dillian deserves it more than Fury because he's been consistent and Wilder because he's the champion".More news: Dramatic changes ahead for Tour Championship in 2019
"We're in the same division, we're in the same era, it would be silly not to fight", Joshua said at a news conference.
"Look, I'm not in the blame game, it was him, it was me, tit for tat".
"I'm a physical, strong guy".
"I would fight all of them. I would fight Fury if he's ready".
Immediately afterwards, former heavyweight world champion Fury, who is fighting Wilder on December 1, took to social media to call out Joshua. Since then, criticism has largely been equal to the praise Joshua has received, including a breakthrough 2017 knockout of Klitschko in which Joshua was forced to overcome both a knockdown and stamina dump that almost cost him the fight.
"We want that fight now, we want him to be the undisputed heavyweight champion of the world".More news: Cleveland Browns Instant Reactions: Baker Mayfield era begins
"It would certainly be the biggest fight in British boxing, we know that because we just had the biggest fight in British boxing with the (Wladimir) Klitschko fight (April 2017)".
When the fight resumed, Joshua showed no mercy and referee Steve Gray jumped in as the champion landed concussive blows after one minute and 59 seconds of the seventh round. We will negotiate the fight now. In terms of April, if we want the fight to happen then, Wilder must win.
Joshua first wobbled Povetkin with a right hand, followed by a left before the telling left hook and right hand sent the challenger crashing to the canvas.
"At this level it's never going to be easy", Joshua said.
"It could have been seven, maybe nine, maybe 12 rounds to get him out of there but the ultimate aim was to be victorious".More news: Rap mogul Marion 'Suge' Knight pleads no contest to manslaughter