Aritz Aduriz's 11th-minute header consigned Real Mallorca to their ninth defeat in 11 league games, but Athletic Bilbao were just as thankful to goalkeeper Gorka Iraizoz for the three points as they moved nine points clear of the relegation zone.
The visitors went in front with their first serious attack as Andoni Iraola's searching cross found Aduriz free at the back post to head home his 11th goal of the campaign.
Mallorca then created countless opportunities to get back in the game but Iraizoz was equal to efforts from Giovani Dos Santos, Tomer Hemed and Victor Casadesus before the break, whilst Victor also fired wide with an open goal after the interval.
Another defeat means that Mallorca's winless streak extends to 14 games in all competitions and this one will arguably hurt the Islanders even more than some of the heavy beatings they have taken in recent weeks, given the quantity and quality of chances they had to take something from the game.
As has been their problem of late, the hosts conceded early as Iraola - back after missing the last few weeks through injury - launched a high ball up to the back post where Aduriz rose highest to brilliantly direct a header back across Dudu Aouate and into the far corner of the net.
Thereafter though it was the goalkeeper at the other end who became the main man as Iraizoz time and again denied Mallorca a route back into the game.
He was first called into action after 16 minutes as he somehow clawed away Dos Santos' goalbound free-kick before getting back on his feet to turn Hemed's follow-up effort wide.
Hemed then pulled a shot inches wide and the Israeli was denied again by Iraizoz seven minutes before half-time as he showed great agility to tip his header from close range over the bar.
Victor also had a shot turned away by the Athletic keeper just before the break, but the Mallorca forward should have brought his side level eight minutes after the break as Pedro Bigas broke down the left and rolled the ball across the six-yard box only for his team-mate to roll his effort wide.
Aduriz was denied a second as his header from Oscar de Marcos' cross produced a fine reaction save from Aoaute and despite continuing to push for an equaliser, the hosts did not create another clear opportunity as they remain just one point and place above the drop zone.