The Catalan giants looked like they were out of the title race after a 2-2 draw with Getafe earlier this month, but both Atletico and Real Madrid's respective failures to win gave them another chance.
Real's defeat to Celta Vigo last weekend saw them fall out of contention, meaning the title will be decided in Barca's game with Atletico at Camp Nou this weekend.
Gerardo Martino's men must win to claim top spot, while Atletico can draw and secure a first league title since 1996.
Xavi admits he thought their chance had gone, but they must now take the chance given back to them by winning the title decider in front of their own fans.
"We thought it was bleak, we thought we had lost La Liga but football has given us another opportunity," the midfielder said on Wednesday. "We are playing at home in front of our fans and we have everything in our favour to win.
"We have a historic opportunity.
"It will be a spectacular final. Anyone who thought we would still have a chance would have been classed as crazy!
"All we want to do is win the league. This is a unique match and I do not know if we will ever experience something like this again."