The experienced midfielder admits his side believed their title defence was over a few weeks earlier and is eagerly anticipating "a spectacular final" on Saturday
The Catalan giants looked like they were out of the title race after a 2-2 draw with Getafe earlier this month, but a defeat to Levante and draw with Malaga means Atletico can still be overtaken by the champions heading into the final day.
Gerardo Martino's men must win at Camp Nou to claim top spot, while Atletico can draw and secure a first league title since 1996.
Xavi admits he thought their chance had gone a few weeks earlier but is now relishing what he believes will be a "spectacular" game 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."