Zaragoza's late push for survival stalled with last week's 1-0 defeat to Mallorca and they now sit six points behind Villarreal with four matches remaining.
That gap is effectively seven points given Zaragoza's dreadful goal difference, which stands at minus 31.
"Everything depends on a win on Sunday," winger Angel Lafita told reporters.
"It is a major victory that would give us confidence for the remaining games.
"It may be a turning point. It is a new opportunity provided and we must seize it. We cannot look beyond Sunday."
Bilbao have their own ambitions this season - they are still in contention for a top-four finish and this week they qualified for the Europa League final.
But Lafita believes Zaragoza's desperation for a result will be greater this weekend - and he demanded his side translate that onto the pitch.
"We are playing for more than a title," he said.
"We're playing for more than them and that has to be seen in the field."
But Bilbao know that a victory will keep the pressure on fourth-places Malaga with fixtures against champions-elect Real Madrid, Getafe and fourth-placed Levante still to come.
Coach Marcelo Bielsa will welcome back the versatile Oscar De Marcos, who missed Thursday's Europa League semi-final second leg against Sporting Lisbon due to a European suspension.
For Zaragoza, forward Carlos Aranda and full-back Ivan Obradovic have both returned to full training and will hope to feature.