Victory at Villa Park on Monday night would establish a six-point gap between the Black Cats and the midlanders with three games of the campaign remaining and all but end their fears of the drop.
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'."
Sunderland looked to be in dire trouble when Di Canio arrived at the Stadium of Light at the end of last month with trips to Chelsea and Newcastle to come ahead of bogey side Everton's visit to Wearside.
However, a narrow defeat at Stamford Bridge was followed by a stunning 3-0 victory at St James' Park, and a first win over the Toffees in 20 attempts in all competitions left the Black Cats looking upwards rather than over their shoulders.
The Italian 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'."
Di Canio has already seen Villa at close hand this season having sent his Swindon side into Capital Cup battle against them in October only to see Christian Benteke snatch a face-saving 3-2 victory for the Premier League outfit with a last-gasp winner.
The 44-year-old was later accused of making a gesture towards the Villa supporters suggesting he believed they would be playing their football in the npower Championship next season, something he continues to deny.
Nevertheless, he is likely to receive a hostile welcome on Monday evening, and it does not bother him one bit.
Di Canio said: "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.
"I played in front of 70,000 singing the worst Italian words at me, and that only gave me more energy.
"But what happened was clear - it was to praise my fans because they were on top, in my opinion.
"We lost that game, a game in which we should have been two or three goals in front. We dominated the game against them.
"I said thanks to my fans. I said to them, 'You were on top. We lost on the field, but you were on top'.
"It was my opinion, it wasn't any bad gesture against the opponents, I just wanted to thank my fans."