Barca looked out of the running for top spot a few weeks ago but with the leading three sides in Spain all stuttering the title has boiled down to Saturday's match in the Nou Camp.
Atletico have 89 points, three more than Barca who have drawn their last two matches, but a win for the hosts would see them retain the trophy courtesy of a better head-to-head record.
"We saw the situation as black and that we had lost the league but football has given us another chance," Xavi told a news conference.
"We play at home in front of our fans and we have all in our favour to win. The crowd need to get behind us due to what we are playing for.
"This is an historic chance and it will be a spectacular final. Anyone who thought that we still had chances would have been considered crazy."
With a first title since 1996 within touching distance Atletico have picked up only one point from their last two games since reaching the Champions League final.
Xavi, however, believes Atletico are still the team in the driving seat.
"It will be very difficult as they are the best team defensively in Europe," he said. "They pressure a lot, work hard together and have different attacking options.
"It will be a rocky ride as they are the team playing best. From five games that we have faced them we have lost once and drawn four. The key for us will be to score early so that they will have to come out."
Xavi said winning the title would be the ideal riposte to those who claimed that the team was in terminal decline.
"We have had a great generation and we can continue to do big things over the coming years," he said.
"It is a tremendous final. It would be the icing on the cake for this generation to win."
(Editing by Martyn Herman)
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