Arsenal used every trick in the book as they hung on to a 2-1 lead for virtually the entire second half with 10 men after Leandro Trossard was sent off for kicking the ball away.
But substitute Stones popped up in the eighth minute of stoppage time to equalise and preserve City's near two-year unbeaten run at home in the Premier League.
It was a huge relief for City who returned to the top of the table, two points ahead of rivals Arsenal who slipped to fourth.
In truth, City looked woefully short of ideas as Arsenal played with 10 men behind the ball, their usual slick passing game bogged down by Arsenal's red wall.
"They've done it for a few years, and we know to expect that," defender Stones, who played more like a centre forward when he came on, told Sky Sports.
"You can call it clever or dirty, whichever way you want to put it, they break up the game and obviously upset the rhythm for everyone. They use it to their advantage.
"I thought we dealt with it really well. It's not easy. When those things are happening, you're trying to gain momentum. You're trying to get a foot into the game and get above them.
"Those little stoppages stop that. We controlled our emotions really well."
Arsenal have become a streetwise unit under Arteta who has twice taken them toe-to-toe with City in title races and for all their attractive football, they have become masters at disrupting the rhythm of opposing teams.
City threatened to blow Arsenal away in the opening stages with Savinho setting up Erling Haaland to fire his side in front with his 100th goal for the club.
But Riccardo Calafiori equalised out of the blue with a stunning long-range effort before Gabriel headed Arsenal in front shortly afterwards.
Everything changed, however, after Trossard became the second Arsenal player this season to be sent off for delaying a restart by kicking the ball away.
He was given a hug by Arteta as he trudged off and the Spanish manager said he was proud of the way his team kept City at bay for so long despite being a man down, even if their delaying tactics were not to everyone's taste.
"We played the game in a difficult context. Playing against the best team in the world." he said.
"Obviously, it is already a miracle we played 56 minutes at the Etihad with 10 men. It is unbelievable what we have done."
