Xavi was amongst a number of players who claimed Barça's chance had gone with a 2-2 draw at home to Getafe two weeks ago, but a remarkable end to the tightest title race in years in Spain in which the top three have failed to win in their last seven combined games has gifted the Catalans a second chance to be champions.
"We thought that we didn't have a chance and perhaps we threw the towel in too soon," said the Spanish international.
"We thought the league was lost, but these things happen in football and now we have everything in our favour to win. It is a very important title and we need to be united. It is a historic opportunity. It will be a spectacular finale."
Victory would secure an eighth league title for Xavi and a seventh for the departing Carles Puyol and Victor Valdes, but he insists the most decorated squad in Barça's history still have the hunger to succeed.
"We have a great generation of players. This is a unique match, a unique opportunity which may never come round again.
"It would be the icing on the cake for this generation to play in such a vital match."
However, to win the league Barça will have to do something they have failed to in five previous meetings this season and beat Diego Simeone's exceptionally well-organised Atletico side.
Barça have managed just two goals in those five encounters and have yet to go in front in any of them, which makes the first goal the key for Xavi.
"They are the best team defensively, the press high, they are solid and attack with variation.
"One of the keys to the game is to go ahead to make them have to come out more."
Neymar is the only Barça player to have scored against Atletico in those five encounters and the club are hopeful that the Brazilian will be fit to feature at some point after over a month out with a foot injury.
Gerard Pique and Jordi Alba have also returned to training, but the match is likely to come too soon for both Spanish internationals.
Atletico are hopeful their own Brazilian-born star striker Diego Costa will be fit after he missed last weekend's 1-1 draw at home to Malaga with a hamstring problem.
Costa is unlikely to be risked if they is chance of him aggravating the injury, though, with the Champions League final against Real Madrid just a week away.
A La Liga and Champions League double would seal the best season in Atletico's 111 year history, but defender Filipe Luis insists they are enjoying the experience rather than feeling under pressure.
"We aren't under pressure, we have a great responsibility. We have overcome very difficult teams in the league and the Champions League and we are in a very important moment in the history of the club," he told the club's website.
"It hasn't been easy, but we have got here with a lot of hard work and now we need to finish off the season in style.
"I think the game will be like the others against Barcelona this season. Barcelona are one of the best teams in the world. They have great quality and almost never lose the ball.
"They are playing at home and know they have the league in their hands, but it will be a game in which we will defend very strongly and look to counter-attack, whilst they'll want possession and control of the game."
There are also issues to be resolved at the bottom on the table as Osasuna, Valladolid and Granada look to avoid joining Real Betis in being
Osasuna must beat Betis to have any chance of staying up and hope Valladolid beat Granada.
Valladolid need to win and hope Osasuna don't to survive, whilst a point will be good enough for Granada to maintain their place in the top flight.
Fixtures (all times GMT)
Real Madrid v Espanyol (1400)
Barcelona v Atletico Madrid (1600)
Valencia v Celta Vigo (1800)
Real Sociedad v Villarreal
Almeria v Athletic Bilbao
Valladolid v Granada
Osasuna v Real Betis
Rayo Vallecano v Getafe
Sevilla v Elche