The Black Cats seemed to be slipping to a damaging defeat when Jonathan Walters put the Potters ahead after only nine minutes and Craig Gardner saw red for a rash lunge on Charlie Adam 11 minutes before half-time.
But their remaining 10 men showed tremendous spirit to outplay their opponents in the second half and got their just reward when John O'Shea's close-range effort secured a 1-1 draw.
The result took them three points above Wigan, who play on Tuesday night, and level with Newcastle and Norwich.
Crucially, though, they have a significantly better goal difference than all three and Di Canio believes that leaves them in charge of their own fate.
"We have got destiny in our hands because we are still in a better position than Newcastle and Norwich," he said.
"We have better goal difference so it is still in our hands if we win our games, but I know that is difficult.
"If we lost this game, even more pressure, and obviously a win would have been different - we would have 40 points already."