Victory at Villa Park on Monday night would establish a six-point gap between the Black Cats and Paul Lambert's men with three games of the season left.
Di Canio said: "If we win on Monday, we stay up. I have told my players, Monday is a Champions League final.
"Since the first day we joined together at the beginning of the week, I told them, 'Take this week as the most important week of the season because if we win on Monday, we stay up and we do it three games in advance.
"'It's probably not mathematical, but we would be very close, so it means that you are capable'.
"I told my players, 'When I came in here, we were nearly strangled - you have turned the season in three games here. You did that, you were capable of winning two in a row.
'If we win the next one, in three weeks, you have turned completely the season'."
The Black Cats were sliding towards relegation until Di Canio arrived but victories over Newcastle and Everton have given them breathing space.
Di Canio said: "It doesn't mean that now we have become a Champions League side, but victory at Villa would mean that with three games to go, we could finish in a good position.
"Obviously, it's step by step, but I told them, 'Think about Monday as a Champions League final, work as hard as you did in the last few weeks because there is a big opportunity to stay in this league with three games to go.
"'Enjoy the last three games and try to get the maximum points we can'. I went to St James' Park without any sort of worry - you can't imagine I would be worried at Villa Park, with all respect."